Talk:Quantum entanglement

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[edit] improve the article

To-do list for Quantum entanglement: edit · history · watch · refresh

Primary:

  • It is necessary to mention *angular dependence* of entanglement. Without it a classical model can explain the results. For example: a red and green ball are each placed in their own leather bags (objects made indistinguishable) and then they are placed in a larger bag and shuffled. One small bag is then thown at Alice the other at Bob. The instant Alice opens her bag she knows the color of Bob's ball. Alice can not predict what color she will receive since the source generates random choices but the two thrown balls are always anti-correlated (differ in color). Entanglement arises when no such classical model can be created for combinations of polarization angles (for example).


Secondary

  • Write a layperson-friendly explanation of what quantum entanglement is.
  • Summarize 2003 experiments mentioned on talk page below.

Please scroll down to read about the dispute.

[edit] early plea for improvement

For example, it is possible to prepare two particles in a single quantum state such that when one is observed to be spin-up, the other one will always be observed to be spin-down and vice versa, this despite the fact that it is impossible to predict, according to quantum mechanics, which set of measurements will be observed.

[edit] transmitting information

(13 Feb 2003) Though I have read the discussion below about transmitting (and not transmitting) information, I am afraid I still don't "get it." Perhaps my brain stumbles on the meaning of "classical" information. To my average mind, "information" would include the fact that the state of a paired photon had changed. If that sort of "information" is detectable, it seems fairly easy to imagine that such transmissions could be scaled up and such transaction could be used to transmit any sort of "information."

What raised the issue is the latest of several New Scientist articles, http://www.newscientist.com/news/news.jsp?id=ns99993384, mentioning entanglement being used to transmit information. I confess I don't fully understand the articles.

In quantum mechanics, the only "information" you can obtain is by performing a measurement. In this case, this is the measurement of "spin". Nothing else can tell you anything about the system, including whether or not "the state of a paired photon had changed." As for quantum teleportation, see that article. -- CYD
I don't fully understand the article either (I'm not a quantum physicist). But is it possible to "scramble" a particle that has already been observed so that its state is again uncertain? Because this would open up a whole new can of worms.
Yes. You use some device to observe (the previous state of) the particle. That device scrambles the state of the particle, so that the state (after the observation) is again uncertain. But that device also causes quantum decoherence, so the state (after the observation) is no longer entangled with the state of the other object. Is there some way we could make this more clear in the article? --DavidCary 18:36, 5 January 2006 (UTC)
I think that by giving a concrete example is probably a better way to understand an abstract concept. A good quantum physics text book should provide many solved examples for the readers. A solved example is helpful to me, but it would be a tedious job for the writer :) -- Justin545 (talk) 02:23, 25 January 2008 (UTC)

Currently the article seems to contradict itself. It implies that entanglement *can* be used to transmit information ( quantum cryptography, and perhaps quantum_teleportation ), and yet *cannot* be used to transmit information ("Although two entangled systems can interact across large spatial separations, no useful information can be transmitted in this way.").

Is there some way to clarify that

  • entanglement might be useful in some communication systems, but
  • one cannot transmit information faster than the speed of light (whether or not one uses entanglement).

? --DavidCary 18:36, 5 January 2006 (UTC)

In reply to David Cary, it can be used to transmit information, but not faster than the speed of light.

Say you have two entangled atoms, one which you have flown to the surface of Mars and one which has remained in your laboratory on Earth. You know that the atoms are entangled, that they have a relationship with each other, but what you don't know is their actual state. You also have no way of predicting what their state is. So when you measure the one, you also know what the state of the other atom is through deduction, but as the states of both atoms change randomly over time this does you no good at all - you couldn't use your measurements to control, say, a Mars rover as the only information "transmitted" by measuring the spin-states of atoms sequentially is random noise, in line with causality preservation and the speed limit on information transfer of the speed of light.

It's like the universe works in such a way as to ensure that cause and effect cannot be mixed up, and that is why nothing, not even information about things, can travel faster than light. --Badnewswade 00:38, 27 April 2007 (UTC)

[edit] "pure", "separable", "mixed"

I corrected a small confusion between the definitions of 'pure' and 'separable' states. [from the Centre for Quantum Computation, Oxford]

Do you have a reference? Several books and webpages I have read, on QC and other topics, simply refer to it as a "pure" (as opposed to "mixed") state. For example, Sakurai refers to a "pure ensemble". -- CYD

Hi. Indeed pure states are opposed to mixed states. But both types can also be either separable or not, and that was the confusion that I tried to correct. If a bipartite state (pure or mixed) is separable then its parts can be produced separately by classically correlated sources. If it is not separable, then the state is said to be entangled, and can exhibit non-locality, contextuality and such counter-intuitive phenomena. A review on separability can be found on http://uk.arxiv.org/abs/quant-ph/0006064 but it is quite technical. I again read through and corrected a few problems arising from this confusion.

A comment on notation: The product Hilbert space of the two particles is the tensor product. However, the notation used on this page is traditionally used, at least within mathematical texts, for the direct product, ie the cartesian product of the sets endowed with the appropriate coordinate-wise notions of addition and scalar multiplication. The tensor product is not the same thing, as can be seen by comparing the correctly-given basis here to the basis of the direct product, which would be a sum over one index, extended to include the separate terms individually, but not as a product. This can be a source of considerable confusion for someone who knows a little about the mathematics of Hilbert space and is trying to figure out how it applies to quantum mechanics.

claim that hidden variables theories can't be local removed

Would you care to comment on why this claim is inaccurate? It seems to me a cogent description of the outcome of Bell's theorem. -- CYD

Then Bell's theorem is wrong.

Many-worlds is a counter-example to the claim. It is a purely local theory which is also deterministic. It is also the quintessence of a hidden variables theory; think of all those worlds which we can never observe. I could be wrong about the locality of many-worlds but most people seem to consider it local in the important sense (that non-local effects are unnecessary to explain the Aspect experiment). -- ark

Many-worlds is local, but it is not a hidden-variable theory in the sense of Bell's theorem. I think the characterization of Bell's theorem was correct. See EPR paradox. AxelBoldt, Thursday, May 30, 2002

I don't think it makes sense to talk about many-worlds being "local", because the Hilbert space of a system need not be the space of square integrable wavefunctions. If I'm not mistaken, that's how non-local phenomena (such as the EPR paradox) come about. -- CYD

Whatever you guys decide, the EPR paradox page needs to seriously change. For example, it says "many hidden variables theories have been constructed" and then says "but experiments sided with QM against them". What theories are they talking about? I don't know and it will seem to most people that it's talking about Many-worlds. That's just one example by the way.

Also, an alternative to interpretating Bell's theorem as saying that Many-worlds is not a hidden-variable theory, is simply to say that Bell's theorem is meaningless because it uses a concept of "hidden-variable" which ultimately interests no one. -- ark

Well, obviously that kind of hidden-variable theory interests no one now. On the other hand, EP&R did suggest that quantum mechanics was incomplete, relying on some underlying classical hidden variables. I'm not actually sure if their suggestion was developed by anyone into a workable theory, but Bell's theorem imposes quite strong constraints on the kind of hidden variable theory that can be formulated while matching reality. -- CYD

Something that physicists (and serious physics students) seem to rarely understand is that the mathematics of physics is a completely different subject from the history of physics, which is still different from the ontology of physics (what exists in reality, what I would call the essence of physics).

And they never understand that you can and should teach these three very different subjects separately. So if Bell's inequality is only of historical importance then it's useless and should never be mentioned outside a class on historical physics, where it would be taught aside other great failures of physics. If there's anything in Bell's analysis that's actually relevant to the ontologies of modern physics theories, then that should be carefully extracted out and the rest discarded as chaff. -- ark

As a student of physics (junior level), i'm right now studying the progress of the EPR paradox through Bell's inequalities and into quantum teleportation. I don't think calling Bell's theorem a failure is particularly useful, in that it does set up a specific test of entanglement and present a way to measure it, which was done directly by Aspect, Grangier and Roger. In addition, going though the history of this debate has helped solidify--as much as possible for QM--my understanding of what we're doing with QM. It's poorly worded, but what i'm trying to say is that physics is in some sense inseperable from a selected study of history. it's by learning what other people did, where they were right and where they were wrong, that you actually come to understand what is going on-- for instance, if EPR were right, then QM wouldn't just be incomplete, it would be downright wrong. AGR fround the opposite, and we can work out some more details from there. Talking about quantum entanglement wouldn't make sense at present if you didn't know anything about bell's theorem; that's my opinion as someone looking at the topic for the first time. If you're worried about people misunderstanding how bell's theorem presently applies to physics, well, it seems like directing them to intelligible resources like the appendix of D.J.Griffiths QM book or Bell's Speakable and Unspeakable in QM is the best path to take. This is my first real visit to wikipedia, so please let me know if i have the right idea about how the site works. --T^3

"Entanglement obeys the letter if not the spirit of relativity"

It's funny to read this given:

The peculiar aspects of quantum spin measurements in EPR-type experiments can be regarded as a natural extension of the principle of special relativity. (http://www.mathpages.com/rr/s9-09/9-09.htm)

The "spirit of relativity" refers to the locality principle, which it's fairly clear was what EP&R were concerned about. The link you provided offers an analogy between quantum measurements and relativity - which is not incorrect, but it's not the standard approach to this problem, AFAIK. -- CYD

Of course, the standard approaches don't seem to be a lot of help to most people, especially non-experts, in understanding physics. So I think that, like other ambiguous stuff that you need to be a physicist (and preferably a historian of physics) to understand, it should just be removed. (Like I did on the Copenhagen page. What do you think of it btw?) -- ark

Someone deleted my previous note that at least one scientist has actually used this to transmit information, based on the "fact" that its not possible to do so. Tell that to him--he'd already done it. Classical music, to my recollection. Anyway, here is a formal piece of evidence thats just cropped up:

http://www.theaustralian.news.com.au/common/story_page/0,5744,4522247%255E2702,00.html

The URL's a little mangled...

--Alan D

Actually, all they did was quantum teleportation, which never transmits classical information faster than the speed of light, and isn't even helpful for sending classical information. One key paragraph is:
An encoded radio signal is embedded on an input laser, which is combined with entanglement and then scanned. The laser is destroyed in the process. But the radio signal survives and is sent electronically to a receiving station, where within a nanosecond an exact replica of the beam - with the radio signal intact - is retrieved and decoded.
Notice that in order to teleport the laser from point A to point B, they had to first destroy the beam, then send radio waves (at the speed of light) from point A to B, then recreate the beam. You could say that the quantum state was teleported instantly, but the people at B couldn't detect that it had been teleported until after the slow radio waves reached them. Point B didn't end up with any more classical information than was already present in those radio waves. Quantum teleportation has been done by a number of people now, but it has never sent a single bit of classical information. -LC, Sunday, June 16, 2002

OK, I misinterpreted that part...I'm certainly no expert :-) I'm wondering now if the thing on the classical music was the same. He explicitly stated however that he was transmitting information using the technique, but it could have been sensationalistic journalism. I wish I could remember where I saw it.

--alan d

If I'm not mistaken, the reference you provided covers a technique called quantum teleportation, which is not what this article is talking about. The article is noting that it is impossible to transfer information using the EPR setup; otherwise, you would be able to send information faster than light. It is possible to transfer information using quantum teleportation, but then the information will not travel faster than light. -- CYD

I find the first sentence of this article potentially highly misleading: The entanglement of two quantum systems that are far apart does NOT lead to them interacting with each other over the distance - at least not within the standard interpretation of quantum mechanics. They just may show correlations that are so strong that, if you want to explain them in terms of a hidden-variable theory (as EPR intended to, for example), this hidden-variable theory cannot be a local theory. For example, in Bohm's h.v. theory (which agrees with q.m. predictions and therefore, according to Bell, has to be nonlocal) one can indeed see how one of the particles is influenced by what the other one does (which may be influenced by the setting of the other detector). But as you point out yourself, it cannot be used for superluminal communication, because the outcomes are statistical, and on the average there is no mutual influence. Since usual QM only talks about statistical results anyway, it is misleading (at least for the beginner) to imagine a superluminal influence appearing between the particles.

How about something like this: Entanglement is a purely quantum-mechanical property of two particles whose physical attributes (like position, momentum or spin) have become correlated after interacting with each other. The correlations between such "entangled" particles may be shown to be stronger than any "classical-like" theory allows, under appropriate circumstances (see below for more details). -- FlorianMarquardt

I went ahead and did something like this. Feel free to make such changes without posting to the Talk page, as that is more efficient. Welcome to Wikipedia, by the way! -- CYD

On the Formalism section - that's a tensor product of Hilbert spaces, rather than cartesian product, isn't it? I wouldn't want to transgress any conventions usual in the topics, but this does seem to be a key point.

Charles Matthews 10:30, 19 Jun 2004 (UTC)

The assertion made in the article that a given state in entangled IFF its reduced density operators are mixed is incorrect. The correct assertion is this: IF the composite system is entangled, then the reduced operators are certainly mixed. However, even seperable composite states can lead to mixed reduced operators. For example, \Rho_(AB) = \Rho_(A) \TensorProd \Rho_(B) where \Rho_(A) and \Rho_(B) are mixed is a seperable state. However, the reduced density matrices, in this case \Rho_(A), \Rho_(B) are mixed. I had made the change a while back, however it seems to have reverted back. Could somone make the change again?

--Chirag —Preceding unsigned comment added by 61.12.4.26 (talk) 06:08, 17 January 2008 (UTC)

[edit] Bell test loopholes

I've added a couple of links re Bell test loopholes recently. Too much has been written about quantum entanglement on the assumption that the experiments have confirmed it convincingly. Re the apparent (limited) success of applications of entanglement, some readers might be interested in an article I've archived [1] that has yet to find a publisher. It seems likely that the real world is producing something useful by way of real correlations of phase and frequency but not otherwise taking much notice of accepted theory. The net result is better described by classical wave theory, adapted to allow for the behaviour of modern beamsplitters and photodetectors. Caroline Thompson 08:42, 1 Jul 2004 (UTC)

Are you saying that quantum mechanics is incorrect? -- Tim Starling 08:50, Jul 1, 2004 (UTC)
As far as the experimental evidence is concerned, there is at present nothing to choose between QM and local realism. Popular accounts that claim local realism has been ruled out by, e.g. Aspect's experiments, are wrong. Which theory is actually right is best tackled, I think, not by searching for "loophole-free" experiments (which several teams are doing) but by investigating more carefully which model fits the facts best in existing setups, when the conditions are modified slightly. If the local realist model (the basic form of which has been known all along) turns out to be superior, correctly predicting the way the coincidence curves will change when you vary, for instance, detector efficiency, then it will have been shown that QM does not work for these experiments. However, the determined quantum theorist will be able to continue to believe that it works for smaller systems. The experiments are in fact macroscopic. (Caroline Thompson 17:21, 1 Jul 2004 (UTC))

I toned down Reeh-Schlieder remark, as I see no much beef in the Reeh-Schlieder theorem for quantum entanglement. RS simply states that the non-local effects aren't exactly zero but vanish exponentially with distance. And it is a very general statement about all states and local operators. QE in QFT would need larger correlations for a smaller set of states. Pjacobi 09:33, 9 Jul 2004 (UTC)

[edit] Experimental proof / scientific consensus

So a few weeks ago, I was listening to MIT Prof. Seth Lloyd on NPR explaining the experiment behind this promo text:

"New research into quantum entanglement by a group of researchers in Austria reveals that two photons can be entangled -- in a strange linked state --without a connection between them, even when the photons in question are on opposite sides of the Danube."

The paper was published in *Science* in 2003 - Aspelmeyer et al., Long-Distance Free-Space Distribution of Quantum Entanglement. You can find it on sciencemag.org, but registration is required. Prof. Lloyd was certainly under the impression that quantum entanglement is real. A free popular-press summary: http://physicsweb.org/article/news/7/6/20/1

Digging a bit further, I also found this press release

February 26, 2003
Michigan researchers achieve quantum entanglement of three electrons
ANN ARBOR, Mich. - The quantum entanglement of three electrons, using an ultrafast optical pulse and a quantum well of a magnetic semiconductor material, has been demonstrated in a laboratory at the University of Michigan, marking another step toward the realization of a practical quantum computer. While several experiments in recent years have succeeded in entangling pairs of particles, few researchers have managed to correlate three or more particles in a predictable fashion.
The results were presented in an article on Nature Materials' web site on February 23 and will appear in the March 4 issue of Nature Materials, titled "Optically induced multispin entanglement in a semiconductor quantum well." Authors of the paper are Jiming Bao, Andrea V. Bragas, Jacek K. Furdyna (University of Notre Dame), and Roberto Merlin.

You can find this article on nature.com, but again, registration is required.

These purported demonstrations of quantum entanglement are more recent (2003) than the experiments in the 1970s and 1980s which the article Clauser and Horne's 1974 Bell test currently discredits. My preliminary sampling of professional opinion suggests to me that the peer-reviewed physics community is of the opinion that quantum entanglement has been convincingly demonstrated. I therefore dispute the claim made on Talk:Clauser and Horne's 1974 Bell test that "[t]here is as yet no convincing evidence that quantum entanglement occurs." I invite discussion of the 2003 experiments and further investigation of peer-reviewed articles and the opinions of professional scientists and engineers, to resolve the dispute. -- Beland 02:41, 17 Aug 2004 (UTC)

I'm not sure that there is not much dispute over the experimental results. It's pretty clear that there no generally experimentally accepted results that contradict QM. You can find lots of loopholes by which you can argue that local realist models are still correct. However, it is also the case that any local realist models are going to have to deal with explaining the phenonmenon that looks like quantum entanglement.

Roadrunner 04:43, 17 Aug 2004 (UTC)

Except for the conflict between QM and General Relativity, I think you mean, no? -- Beland 01:23, 19 Aug 2004 (UTC)
That's theory and not experiment. The current state of place is that there are no known experimental results that conflict with QM. There are also no known experimental results that conflict with GR. Now it is true that at high enough energies, QM and GR conflict with each other. Unfortunately those energies are so high that we can't do an experiment.

Roadrunner 03:51, 21 Aug 2004 (UTC)

This is a difficult situation. I know full well that the physics community will tell you that quantum entanglement has been experimentally confirmed, but I have more complete information on the subject than most.
I think its necessary to distinguish the phenonmenon of "quantum entanglement" from quantum mechanics If you define it as the the phenonmenon by which the observed state of one particle is correlated with the observed state of a distant particle, that is definitely been observed. What isn't completely solid is that QM or something mathematically equivalent is the only possible explanation for the phenonmenon.

Roadrunner 03:51, 21 Aug 2004 (UTC)

I know, for instance, that the tests used in these modern experiments have the same loopholes as the CHSH one. They are not valid since they depend on the assumption of "fair sampling". To see why this assumption is not reasonable, I do urgently suggest that you look at my 1996 paper or one of several on my web site or the quant-ph archive, e.g. http://freespace.virgin.net/ch.thompson1/Papers/TheRec/TheRecord.htm/ or http://arxiv.org/abs/quant-ph/0210150 . I need to put my basic "Chaotic Ball" diagrams in wikipedia.
Meantime, as Roadrunner says, local realist models need to explain what is observed, which does, I admit, look remarkably like the text book "entanglement". This can be done, but requires a different model of light and a different way of modelling the output from a nonlinear crystal in "parametric down-conversion" (PDC). The only paper I have on the subject, though, is my own unpublished one, at http://arxiv.org/abs/quant-ph/9912082.
I have been discussing these issues with the professional community for the past 10 years! If you notice, Shimony (of CHSH fame) references my 1996 paper in his new article at http://plato.stanford.edu/entries/bell-theorem/ . He does not anywhere claim that there is convincing evidence. He is currently placing his money on Fry et al's ideas for a "loophole-free" experiment. Tittel referenced one of my quant-ph papers in one of his articles on long-distance experiments in Geneva. But my ideas on PDC do come under the heading of original research, so I realise I can't mention them in the articles here. A pity! Some day, when the community eventually realises what the basic fair sampling loophole is all about, they will start looking again at what really happens and classical ideas on the behaviour of light resurrected and updated.
Actually, I think that what will turn heads is an experiment which produces an unambigious result that cannot be explained by QM. Since local realist models are incompatible with QM, then there should be a way of producing an experiment which conflicts with QM. I have a suspicion that this experiment probably has nothing to do with Bell's test. Also, I have a strong suspicion based on history that if this happens it will start with something weird experimental result that no one has any idea is connected with this issue.
What I was planning to do was after you get done with the Bell test loopholes, to point out why despite them, the physics community still largely thinks that QM is correct.

Roadrunner 03:51, 21 Aug 2004 (UTC)

Roadrunner 03:51, 21 Aug 2004 (UTC)

Caroline Thompson 08:52, 17 Aug 2004 (UTC)

[edit] SPDC

Amir Aczel's book mentions Parametric Down-Conversion; he also mentions how Aspect was unable to create a completely random source and had to create a periodic source from the lasers. That note in fact bothered me; how is it possible to claim complete collapse of a wave function when the source comes from continuous lasing. Ancheta Wis 20:26, 17 Aug 2004 (UTC)

Aspect did not use SPDC, he used an atomic "radiative cascade", stimulated not by periodic laser pulses but by two continuous laser beams. It sounds as if Aczel got it a bit wrong. I don't pretend to know anything much about quantum theory, so can't comment on the collapse of the wave function. I have my own ideas about what really happened in Aspect's experiments, having read his PhD thesis, which gives a lot more detail than the published reports. See some of my ideas in http://arxiv.org/abs/quant-ph/9711044, or my page on local hidden variable theory.
Caroline Thompson 20:45, 17 Aug 2004 (UTC)

[edit] Disintangling Bell's theorem and quantum entanglement

I did some work trying to distangle Bell's theorem from the topic of quantum entanglement. It's really easy to observe quantum entanglement. It's also really easy to come up with a local realist theory that explains quantum entanglement. However, that theory will give different predictions than QM, and the hard part is to observe those differences in an airtight way.

Caroline Thompson 10:03, 21 Aug 2004 (UTC) I don't think experiments will ever be airtight, but a combination of experiments and theory should eventually do the trick. Experiments could easily put the QM predictions in trouble. It's not that I would not expect QM to come up with some modification that would cover any experiment. It is a very flexible theory. If, however, you change the conditions for a Bell test experiment, it is very much easier to modify the corresponding hidden variable model than the quantum mechanical one. As it stands, the basic QM model does not cover easily (or covers but unless modified makes wrong predictions for):
Failure of rotational invariance
Asymmetries of various kinds
Variations in beam intensities
Use of different makes and/or settings of photodetectors
Indeed, one of my main grumbles is that one cannot find published the basic facts about the behaviour of photodetectors: how they really respond to changes in input intensity. Perhaps I have not looked hard enough, but the impression I get is that it is universally assumed that the response is exactly proportional — this despite known facts about dark counts when the input is zero and saturation when it is too intense.

Put briefly. Demonstrating that quantum entanglement occurs is easy. Demonstrating that quantum entanglement occurs in a way that local realist theories cannot explain is a much more difficult. This is an important distinction because I don't think that any of the experimental papers cited here did the latter. Also, I don't think that any of the real world applications of entanglement have anything to do with Bell's test (i.e. quantum cryptography would work fine even if QM was wrong in its details.)

Caroline Thompson 10:03, 21 Aug 2004 (UTC)Yes, I know, and in fact even some of the things they do in relation to the development of quantum computing does not really need entanglement. Ordinary correlations would do.

Keep in mind that it took people about 40 years to figure out that you couldn't explain entanglement with a local realist theory.

Roadrunner 07:44, 21 Aug 2004 (UTC)

[edit] General Comments

Perhaps some kind soul could write a non-formal section explaining how particles become entangled and some of the interesting effects of entanglement. I am sorry to say that this article is incomprehensible to those of us who are not students of physics or who have had but a single year of college physics. I am also sorry to say that it seems to have gotten less comprehensible over the last year or so.

I realize that part of the reason I find this article so difficult to understand is the result of precision. Unfortunately, that precision has become excruciating.

I'm afraid the reason the page is incomprehensible is that it tries to explain something that does not actually happen! It reproduces some of the QM formalism, which, at the end of the day, is not based on any physical assumptions about how the entangled particles could possibly stay entangled. The fact is that there is no experimental evidence for entanglement that holds water. No actual experiment has ever violated a Bell test in "loophole-free" conditions, and every experiment I've looked at (which is quite a number) has had a fairly obvious alternative explanation in terms of ordinary variables, such as polarisation direction or phase difference, that are simply shared by both photons. Yes, lots of experiments reproduce the QM prediction, but, since local realist models can do the same (within the limits of experimental error), does this prove QM right? See Bell's theorem and linked pages, especially Bell test loopholes, Bell test experiments and Local hidden variable theory.
Some of the applications of entanglement may well bear fruit, but this does not prove the theory behind them is correct. They in fact all depend on some of the classical properties of light such as interference, together with some interesting correlations in the light output by Spontaneous parametric down conversion (the process whereby you get two lower-frequency photons output from a nonlinear crystal pumped by a laser). The apparently wonderful correlations seen are the effect of the combination of these physical properties with some algebraic, logical and geometrical facts related to the behaviour of ratios of counts when the things being counted have been selected by chosing only coincident pairs.
I'm not surprised that a year of a physics course is no help in understanding the page! A lifetime would not be enough to truly understand entanglement. The human mind is only capable of understanding something logical. It can learn the "facts" of QM by rote, but Bohr was merely stating the truth when he said that, effectively, if you think you've understood it you're wrong.
Anyway, I'm afraid that as things stand the only way to find out (some of) what really happens is by reading some of the articles on my web site or on the quantum physics archive. Several now cover the subject of the |Chaotic Ball model, which is, as even some experts agree, probably the best way to illustrate the above-mentioned logic, geometry etc.. No physics course covers the local realist approach. You will be lucky if they even mention loopholes.
Caroline Thompson 09:02, 1 Sep 2004 (UTC)
It's my understanding that the current mainstream scientific consensus is that quantum entanglement does happen. Have you looked at the 2003 experiments I referenced? -- Beland 01:18, 3 Sep 2004 (UTC)
I agree, BTW, that a layperson-friendly explanation is both possible and needed. -- Beland 01:20, 3 Sep 2004 (UTC)

I've looked at one of the press releases you gave, re

Jiming Bao, Andrea V. Bragas, Jacek K. Furdyna and Roberto Merlin, "Optically induced multispin entanglement in a semiconductor quantum well", March 4 issue of Nature Materials.

The experiment looks fascinating, but they seem to be using the word "entanglement" to mean just ordinary correlation. There is no mention of having done a Bell test to establish it. Instead the press release says:

"In the experiments, the signature of entanglement involving m electrons is the detection of the mth-harmonic of the fundamental Zeeman frequency in the differential reflectivity data."

But at the end of the day it will be just such ordinary correlations that will be used in what they will call "quantum computing", which will never really use the kind of entanglement that can infringe Bell inequalities since this kind simply does not happen. We're at an impasse, I'm afraid. I should love to re-write the page but my version would not be about "quantum entanglement" as quantum theorists understand it. Their version exists only on paper and in their formulae.

Incidentally, I've read: M. Riebe et al, “Deterministic quantum teleportation with atoms”, Nature 429, 734-737 (2004) which was in the news recently. Here they establish entanglement by measuring "fidelity" which, they say, cannot exceed 66.7% under local realism. What, however, is one to make of this?

" ... obtained fidelities range from 73% to 76%. Teleportation based on a completely classical resource ... yields a maximum fidelity of 66.7% ... Note, however, that to rule out hidden variable theories, a fidelity in excess of 0.87 is required ..."

So they've established entanglement but not ruled out local realism! That's nonsense. I have not been able to find out quite what "fidelity" is, but judging from the context it seems to be much the same as "visibility", and tests based this depend on the assumption that the system obeys Malus' Law. I suspect that they never check this thoroughy. Caroline Thompson 09:13, 3 Sep 2004 (UTC)

[edit] idea for faster-than-light communication

I have an idea: Since by adding/taking any energy into one entangled particle would add/take away from the other, this would warp the fabric of gravitational spacetime. If you did this, you'd be able to measure this (perferably) infintesimal gravitational pull by placing a network of lasers and ultra-sensitive sensors, you might tell if data is sent. since this is minutely economical, you'dd want it in a sattelite or something of that sort. Iamdalto 09:13, 3 Sep 2004 (UTC)

I think this is a great idea. The government must fund it. —Preceding unsigned comment added by 200.122.104.131 (talk) 20:58, 1 January 2008 (UTC)

[edit] External link may need to be *removed*

The external link provided at the end of the document titled "Quantum Entanglement For Dummies" I believe needs to be reviewed for credibility and accuracy by someone with a better understanding of this phenomenon. What I find disturbing is the aforementioned site refers the reader to the following article(towards the end just before his appendix): http://www.rednova.com/news/stories/1/2004/08/09/story001.html

From my understanding the author of this article is basing this idea on a gross misinterpretation of numerous facts and quantum entaglement it self. If the author of the page the external link points to found this to be a valuable resource I would question the judgement of that author and the wisdom of linking to this page, and thus indirectly having wikipedia endorsing something which amounts to science fiction.

However, note I have not done this myself. I am an undergraduate physics student and I am recommending that someone with some kind of credentials (better than mine) in this field review my suggestion and remove the link if my supposition is accurate. I feel it would be irresponsible for someone with my level of knowledge in the field to be editing an article on quantum entanglement.

Yes. Please remove it. Unfortunately, however well-intentioned the author of that article may have been, rather than being "Quantum Entanglement For Dummies" that page is "Quantum Entanglement by a Dummy". CSTAR 17:43, 4 Mar 2005 (UTC)
Oh, okay, sorry about that. Guess I didn't do enough checking first. Cal 1234 15:23, Mar 8, 2005 (UTC)

[edit] Quantum Entanglement Illustrated

Hi,

The external link provided at the end of the document titled "Quantum Entanglement For Dummies" I believe needs to be reviewed for credibility and accuracy by someone with a

The document has been reviewed by many physicists with good knowledge of entanglement, including: Anton Zeilinger, Lov Grover, Helen Quinn, Anthony Seigmann, and Dr. Amir Aczel. If you'd like more, I can list other people and provide both contact information and their credentials. If you want someone else, then find someone else and e-mail the link. I'd be more than happy to change anything that isn't as technically accurate as it could be (which, by the way, is stated in the document), while maintaining my ultimate goal of having it readable by a general audience.

As far as I can tell by reading the article, in particular the comments attributed to them, saying the article has been "reviewed" by these people is a bit of a stretch. If you can point me to a website where said reviews exist, it would be helpful. Please see comment below about non-functioning link. --CSTAR 21:36, 2 Apr 2005 (UTC)

site refers the reader to the following article(towards the end just before his appendix): http://www.rednova.com/news/stories/1/2004/08/09/story001.html

First, why not ask me to remove the link? It is, after all, just one of many that I read. And, by the way, the page does not say the links are a valuable resource. It merely lists them in an appendix.

Second, you folks seem to forget that many things that seemed science fiction have become science fact. For example, using quantum entanglement for instantaneous communications seemed to be in the realm of science fiction -- Mother Nature was going to keep her secrets to herself. Using adiabatic perturbations of quantum particles, it may be possible to influence the statistics of the radioactive decay in a quantum entangled system.

misinterpretation of numerous facts and quantum entaglement it self. If the author of the page the external link points to found this to be a valuable resource I would question the judgement of that author and the wisdom of linking to this page ...

Powerfully astute logic: Judge the author based a single link, rather than judging the document as a whole. FYI: http://en.wikipedia.org/wiki/Strawman

Yes. Please remove it. Unfortunately, however well-intentioned the author of that article may have been, rather than being "Quantum Entanglement For Dummies" that page is "Quantum Entanglement by a Dummy". CSTAR 17:43, 4 Mar 2005 (UTC)

It's nice to see people being judged and summarily attacked.

However, even if I was a "dummy", this once again judges not the document for its content, but the author. These are two totally different logistical arguments. Do try to keep them separate.

Your referring to potential non-expert readers as dummies is no better (nor worse) than my referring to you the author (who states clearly his non-expert status in the article in question) as a dummy. If this is offensive, then I apolgize, but please change the name of your article. -CSTAR 21:36, 2 Apr 2005 (UTC)

And, for the record, is it too much to ask for a wee bit of maturity here?

Lastly, I noticed on a related page a call for an introduction to quantum entanglement for a general audience, which my document provides. It is not intended to be 100% technically accurate given that it is an ``introduction`` for the masses.

Remember labs in high school physics where wind and friction were not taken into consideration? My document is to get the point across, explain some basic physics, without mucking in technical details. And it does this astoundingly well, thank you very much.

Dave

I'm not going to comment about anything else in this discussion, but I'm fairly certain the following is false:
using quantum entanglement for instantaneous communications seemed to be in the realm of science fiction -- Mother Nature was going to keep her secrets to herself. Using adiabatic perturbations of quantum particles, it may be possible to influence the statistics of the radioactive decay in a quantum entangled system.
I'm not sure if this is referring to the quantum zeno effect, but in any case I'm almost completely certain that you won't be able to use it for instantaneous communications. But I don't see what this has to do with your website being factually inaccurate (or not). -- CYD

CYD,

My statement about stimulated triggering particles for instantaneous communications is partially based on the following:

http://www.arxiv.org/abs/physics/0503052

Their article has yet to be peer-reviewed, however their results look promising.

My main point, however, is that the external link to my site was removed for these main reasons (please correct me if I'm missing some, or have misrepresented them):

  1. The accuracy is in question
  2. There is a link to a related site whose content is quite questionable

I believe having Prof. Anton Zeilinger (http://www.quantum.univie.ac.at/) vouch for the site should be sufficient.

That link doesn't work. --CSTAR 21:36, 2 Apr 2005 (UTC)

The "related" site link in question can be removed quite easily.

Lastly, Google currently ranks me at #2 -- below Stanford and above Wikipedia. I figured adding it to Wikipedia would improve the general understanding of quantum entanglement for the masses. Apparently people disagree. Fine with me. :-)

Have a good one, folks. Sorry we couldn't find a little synergy.

Dave

Umm, the preprint looks to be about plain old quantum teleportation. You can transmit information that way, but not faster than light. -- CYD

[edit] cause of entanglement

i dont understand why if a particle is observed to be spin up the other one must be down, what causes that?

Because that's the way it actually woks when you try it in real life. QM is used as the explanation for how this "real life" works.linas 21:41, 5 January 2006 (UTC)

[edit] Cause of entanglement #2

I don't understand why quantum entanglement would necessitate "spooky action at a distance"... Isn't it possible that the "entangled" photons are just behaving deterministically and thus appear to be interconnected without actually being so? Rōnin 02:41, 10 December 2005 (UTC)

No, if they did behave deterministacally, it would violate Bell's inequality. This idea you propose is called local realism, and Bell's inequalit demonstrates that lcal realism is incompativble with QM. 21:39, 5 January 2006 (UTC)
That isn't quite what I'm proposing. I'm asking whether the two photons could simply behaving deterministically, which isn't incompatible with the idea of local realism, but isn't dependent on it either. Imagine that I have a green ball and a yellow ball and hide them under two cups. If I discover the green ball under one cup, I can assume that there will be a yellow ball under the other because the two balls always have a different value, without invoking quantum mechanics. One could imagine that something similar could happen when one splits photons. I realize there may be good reasons for assuming the photons are really interacting across a distance, and it's those reasons that I'm inquiring about. Rōnin 22:33, 10 January 2006 (UTC)
This is exactly what "local realism" is. Local realism says that, under one cup, the ball "really is yellow", but we won't know till we look. I'm not sure what the article on local realism states; if its not clear, then I guess it should be fixed. Maybe this needs to be clarified hree too? Anyway, this is why non-physcists like local realism: QM states that the ball really really is green and yellow "at the same time", until you look, and some people really hate that. linas 00:29, 11 January 2006 (UTC)
Slight correction, linas: the ball cannot be said to be either green or yellow till you look at it. Dave Kielpinski 14:32, 11 January 2006 (UTC)
But does anyone know why the explanation provided by quantum mechanics is preferred over the one I just proposed? Stating that it's incompatible with quantum mechanics is rather obvious, but it doesn't provide any explanation. Rōnin 14:19, 14 January 2006 (UTC)
Because local realism predicts different outcomes than QM for certain experiments; those experiments have been performed, and QM "won". The two predictions are compared in Bell's inequality. Your green/yellow shell-game example predicts the same answer as QM when the polarizers are aligned; but if they are off at a different angle, the predictions differ significantly. linas 20:05, 14 January 2006 (UTC)
Ah, thank you. What we need is obviously a ban on unaligned polarizers, then. ;) Anyway, thanks for humouring me. This issue is such an interesting one. Rōnin 17:17, 15 January 2006 (UTC)

[edit] Quantum Entanglement not violating speed of light

The reasons why Quantum Entanglement can't be used to transmit information faster than the speed of light are really subtle (and really interesting!). This is just another plea for an expert to step in and explain this as well as possible. And no, I'm not even close to being that expert -- I just think it's probably the most important concept in this whole article.

-- Perhaps the best plain-English explanation of why QE cannot be used to transmit information faster than the speed of light, and also why Quantum Teleportation cannot be used to transmit information faster than the speed of light as well:

Photons cannot exceed the speed of light.

Think of it this way: Point A, the origin point where the photon(s) is (are) born, encodes some information on it (them) as spin. The photon(s) then travel (according to our frame of reference) at the speed of light to it's (their) respective destination(s), Point B (and Point C), where it (they) is (are) measured.

To our frame of reference, information is transmitted from point A to point B( and perhaps C). Information is never transmitted between point B and point C - they are receiving copies of what is transmitted from A. Point B /does not/ get to choose which way it modulates the photon, which would allow it to transmit information to C - it only gets to choose which way it measures the photon. C gets to choose which way it measures the photon as well. Whether they do so "correctly" for the purposes of decoding what was sent by A is a side issue.

The confusion comes up because B can know what state the photon at C will be by measuring its' own photon. This produces a human illusion known as the "speed of bad news". If two people read the same newspaper story, and come to the same conclusion, was information transmitted between the two? No. It can be /thought of that way/ - it doesn't mean it actually is.

Further, to complicate things - in the frame of reference of the photon(s), zero time elapses between creation and destruction (measurement), and according to quantum mechanics, they may be thought of as the same particle because they share the same frame of reference. This does not mean they /actually/ are the same particle.

This brings forth the confusion of thinking of them as /actually/ being the same particle in the minds of many people.

To whit: Quantum mechanics is a descriptive theory, and (as has been stated before) is counter-intuitive. Be careful to separate what is described and what is predicted by the model.

-- The "spooky action at a distance" is a function of the system as well - another "speed of bad news" illusion. To the frame of reference of the photon(s), its' (their) state(s) are set at creation, which also happens - to their frame of reference - to be the same as destruction (measurement). The photon(s)'s frame of reference is linked between the 'creation' point and the destruction point(s). To our frame of reference, it still takes time, and "different amounts of time", for the photon(s) to reach their destination(s). One could think of it as taking some time for point C to reach the frame of reference of the photon(s).

As far as the photon's frame of reference is concerned, it involves no distance and 'time' is irrelevant.

It still requires a "conventional" channel for points c and b to discuss their measurements.

[edit] entanglement vs. decoherence

Asking "How can I keep these 2 particles entangled as long as possible?" is the same as asking "How can I delay the decoherence of these 2 particles as long as possible?", right?

Yes, that is right. linas 21:36, 5 January 2006 (UTC)

Would it make any sense to merge quantum entanglement and quantum decoherence into a single article?

--DavidCary 18:36, 5 January 2006 (UTC)

Naively, yes; in practice, no. That's because then you'd have one article that's twice as long. These are related ideas, but, already, one can say quite a bit (and more) about each. linas 21:36, 5 January 2006 (UTC)

[edit] q. crypto ...

I think that the comment "quantum entanglement is the basis of ... quantum cryptography" is a little too strong - the photon polarisation model of q.crypto doesn't depend on entanglement.

It's possible to use entanglement instead of polarisation to build a q.crypto system, but I don't think it's fair to say it's the basis of it ... (unsigned comment from User:YojimboSan 17 January 2006)

I fail to understand this comment. Aren't the polarized photons entangled? There's no crypto encoding unless both parties receive a message encoded with the same key, viz. a pair of entangled photons. The polarization of a photon is its spin. The details for photon entanglement are ever so slightly more complex than the case for spin-1/2 described in this article, but its essentially the same thing. linas 05:55, 18 January 2006 (UTC)
Not quite, linas. The BB84 quantum crypto protocol only requires polarized single photons to be transmitted, not entangled pairs. The secrecy of the key distribution arises because any eavesdropper increases the polarization noise in the channel. The noise can be detected by looking at the correlations of a subset of the transmitted information. So you always know when an eavesdropper is present. Dave Kielpinski 12:31, 25 January 2006 (UTC)
Ahh. Right, thanks. linas 14:27, 25 January 2006 (UTC)

[edit] Unanswered questions?

Maybe these will be considered silly questions, but I really want to understand this concept:

1. Are the entangled particles considered to be in a state of quantum superposition before a measurement on any of them has been conducted?

2. I found some confusion on this subjects by non-physicists - if one of the particles, after being measured, is having it's quantum state altered (if actually possible or only theoretically), will the entangled particle reflect that change?

Thank you! Nate --85.64.39.51 23:51, 30 April 2006 (UTC)

Reply:
1. superposition should not be confused with entanglement. any quantum state is, in general, a superposition.
entanglement is possible only in a composite system. superposition says quantum states are elements of a linear space. entanglement has to do with property of tensor product of linear spaces. not the same.
2. not quite clear what you're asking. take the simplest case. if you have a separable pure state P \otimes Q, and you perform a local measurement on, say , the second subsystem. then Q would, in general, collapse to some eigenstate of the observable you're measuring. clearly the composite state now changes as well.
Mct mht 00:15, 1 May 2006 (UTC)
Thanks for the reply. I got the picture on the first issue, apparently I have misunderstood the Quantum State term.
2. I have explored several websites and there were quite a few that made this kind of assumption about Quantum Entanglement:
Assuming you have a pair of entangled particles. Now one of the particles has been measured, therefore we now know the value of the other entangled particle as well. But then (after the measurements have been done) we go and change the properties of one of those particles. Will the other entangled particle reflect that new change in properties?
Nate --85.64.39.51 00:53, 1 May 2006 (UTC)
more technical details and context is needed in your question for a precise answer. the phenomenon you speak of is not an assumption. it's a physical fact. take a typical example. say a composite system is in a bell state(therefore maximally entangled) and a local measurement(say in the z-axis of the first subsystem) is performed. part of reason that, after that measurement, you can infer from the state of first subsystem that of the second is that, after measurement, the composite system collapses to a product state, i.e. separable. once the composite system is in a separable state, i.e. once entanglement is broken, what you do locally to one will not effect the other. Mct mht 01:31, 1 May 2006 (UTC)
Ok now I understand perfectly. So In fact the process of collapsing the system to a product state by it's nature breaks the entanglement. This should be noted in the article. Browsing the net I found that many simple-minded persons tend to misunderstand this "entanglement" as some kind of "supernatural" link between the particles where they can "read each other's mind" on a regular basis, which obviously is not the case ;)
Nate --85.64.39.51 01:56, 1 May 2006 (UTC)
the existence of entanglement simply follows from the fact that, given two linear spaces V1 and V2, not every vector in the tensor product V_1 \otimes V_2 takes the form v_1 \otimes v_2 for some v_i \in V_i. those nonproduct states are called entangled. Mct mht 02:12, 1 May 2006 (UTC)

[edit] spukhafte Fernwirkungen (spooky action at a distance) - citation?

Almost every article I've read on entanglement (including this wiki entry) contains this quote from Einstein, but I've yet to come across any article that contains a citation of the quotation's original printed source. Does one even exist, or is this just something that Einstein was once heard to say? I actually need to find the original reference for this, so I'm grateful for any illumination.

[edit] Suggestion to merge with Quantum coherence

The Wikipedia has articles on Quantum Entanglement as well as Quantum Coherence. Both these are basically the same concept. So there should really be only one article. Unfortunately, at present the two articles do not even cite each other. Even if I am wrong, and the two concepts are not identical, at least they are very closely related to each other. I will look forward to other people's comments on this point. —The preceding unsigned comment was added by 220.227.48.17 (talk • contribs) .

I moved your comment to the bottom to keep it in chronological order, and I added templates to the articles to get more attention. I think Quantum coherence should be merged into this article or Coherence (physics), but I'm not sure which. —Keenan Pepper 23:39, 22 September 2006 (UTC)

[edit] Question to Which I Can't Find the Answer Elsewhere

Say you have streams (A and B) of polarization-entangled photon pairs. You put a polarizer at 0 degrees in the path of A and one at 90 degrees in the path of B, then measure the correlations of pass / no pass between each pair.

Does classical physics predict a 50% correlation?

What does QM predict? What is the simplest explanation for it?

What if the angles are 0 degrees and 45 degrees instead?

As I understand it, the interesting thing is that classical physics says that there should be no correlation between the two particles what-so-ever! In other words, whether or not one particle makes it through one of the filters should have no bearing on the other, but that's not what happens. There is no framework for entanglement in classical physics, at least not of the quantum kind, for once particle A passes through the filter, if it passes first, it immediately affects particle B. I don't remember the exact percentage, but I think the idea is that if particle A passes through the filter, particle B will either pass or not pass 50% of the time as well (depending on the polarization). Hope that helps, hopefully someone more knowledgeable in this area than I will be able to explain it better. -- itistoday (Talk) 04:02, 20 December 2006 (UTC)
Actually, let me revise that statement. In your example, if photon traveling down path A passes through the filter, then the other photon will not pass through the filter when the angles are 90 degrees. When they are 0 and 45... I'm not sure, but I think that there will be a 50% chance, or whatever is given by that cosine polarization-filter formula. -- itistoday (Talk) 21:17, 16 October 2007 (UTC)
not an experimental physicist but here's a reply. in classical physics, there is no such thing as two entangled particles---think of two ping pong balls, whatever you do to one will not affect the other.
as for the question, say your entangled pair is in the state (|0>A |0>B + |1>A|1>B)/ √2, where |0> and |1> are two orthogonal polarizations: 0 and 90 degrees. suppose, as you say, a 0 degree polarizer in put in the path of A. this amounts to a local measurement on the subsystem A. the possible outcomes of this measurement are easy to list: |0>|0>, |0>|1>, |1>|0>, and |1>|1>. (notice that irrespective of the outcome, the pair would be no longer entangled after this measurement).
the probabilities of each outcome are dictated by the initial state. in our case, we get 50% |0>|0> and 50% |1>|1>. so there's 50% chance that particle A will either pass or not pass. in case particle A passes, we know for certain that particle B has "collapsed" to the |0> state, i.e. it is polarized in the 0 degree direction. (the fact that the initial state is entangled might be worth emphasising. we have only interacted with particle A, but due to entanglement, the state of particle B has now "changed.")
now, still assuming A passes, if you put a 90 degree polarizer in the path of B, QM predicts that it will not pass, with 100% probability. the case when A doesn't pass is analogous: particle B will pass a 90 degree polarizer with 100% probability. Mct mht 07:34, 20 December 2006 (UTC)
This is a multi-paragraph reply
In classical physics, there is no such thing as entangled photons. In the classical view, a photon has an angle of polarization and its odds of passing through a polarizer are cos^2(theta) where theta is the difference in angle between the photon and the polarizer. If the photon passes, then thereafter its own polarization angle is the same as the polarizer. You could in theory set up an experiment where a source spits out pairs of photons that have identical but random polarization. This is the classical physics analogy to entangled photons that causes so much confusion. If you were to do that, and pass each photon through a polarizer set at the same angle, you'd get no correlation in results. Basically it would boil down to each photon having a 50% chance of passing through. This is the probability you get if you average the probability over all possible angles for the photons. So, 25% of the time they would both pass through, 50% of the time only one would pass through, and 25% of the time they would both be absorbed.
When the photons become entangled, then QM's prediction of the rate of correlation of the measurement results changes to cos^2(theta) where theta is the difference in angle between the two *polarizers*. So, when both polarizers are at the same angle, and the photons are entangled, the correlations are 100% (the cosine squared of 0 is 1) -- 50% of the time they both pass through and 50% of the time they are both absorbed.
The difference between the two sets of results is what Bell's Inequality is. The results with entangled photons mean we have to break at least one key assumption about how the universe works in order to make sense of it. Either the future affects the past, or paradox is possible, or the universe is deterministic. Why? Well, picture it. Say your pairs of photons are entangled and your measurement angles are the same. If you measure A and it passes through, then you know B will pass its detector, or will have passed through if it was already measured. This means that your measurement of A will have had to somehow guaranteed that B will pass through its detector. Either your measurement of A propagated backwards in time to when the entanglement was created, or it somehow instantaneously changed B faster than light. —Preceding unsigned comment added by 207.114.255.2 (talk) 18:56, 16 October 2007 (UTC)
While true, one could perhaps make the claim that you are comparing the "entangled photons" model versus the semi-classical case of non-entangled photons. If light is considered entirelly classical (as in classical electrodynamics) then the formula indicates the proportion of light going through the polarizer and not the probability of individual photons going through. When performing actual experiments the result that would come out of this third case should perhaps also be taken into consideration.Agge1000 18:55, 26 October 2007 (UTC)

[edit] Superluminal Communication

Can someone see if they can find any problem with this paragraph and the idea:

For example, in a Bell-state Quantum Eraser (see joot.com), if the polarizing lens is rotated, the interference field will instantly disappear at both detectors. Thus, it may be possible for two people at huge distances to communicate at superluminal speeds if they have a midpoint that constantly transmits polarized, entangled beams at both detectors. The only limitation would be the time it takes to start the communicator, which would be half the time it takes for light to travel between the two detectors. Afterwards, instantaneous communication could be possible by an alternating stream of interference fields and noninterference fields, like Morse code.

Awesomepenguin 02:24, 2 January 2007 (UTC)

Hi, sorry, but without reading any of that I can tell you it's not possible, no amount of justification will let you send information faster than the speed of light. Trust me, it's been tried by very very smart people, and all have failed. In addition to violating several fundamental physical theories, it would also create a paradox by allowing you to send somebody an answer before they asked you the question. Check out the book "Schrodinger's Rabbits" for more. -- itistoday (Talk) 03:38, 2 January 2007 (UTC)
 : Whhhyyyyyyy? :-)
 : Seriously, if polarising light changes it's quantum state, then if you polarize one entangled photon the other will be polarised too...? It might be theoretically impossible, but from an engineering point of view it sounds extremely plausible. What it boils down to for me is that if you can deliberately change the spin / quantum state of an entangled object, then you can use that to transmit information... unless of course the act of measuring it's entangled twin also destroys the information you've "sent". Probably does, actually. Is this correct?
 : Please don't hit me, I'm a layman!
 : --Badnewswade 00:48, 27 April 2007 (UTC)
It does seem kinda strange, doesn't it? But then Quantum Physics always does to we laymen. For example, I don't know nearly enough to know WHY you could send a message to the past. Mostly, I think it's the way the explanations have been, to be frank, dumbed down; the way it's presented, you do something to one particle and the 'entangled' particle does exactly the opposite at precisely the same time with no known anything connecting them (here of course lies the confusion. A layman could, for instance, visualize a doorknob turning and so the opposite doorknob turns in response, without any intervening machinery. Those of you who, unlike me, understand quantum mechanics (or who, like myself and Socrates, understand we know nothing about it) can see the problems inherent in this mindset.) Clearly, this explanation is flawed, because it appears action done to one particle can also affect the entangled particle before it happens, which is no where mentioned in the explanation given to laymen. Bah! I should take a class. I'd probably be LESS confused than I would be with the laymen explanations. I don't even want to think about what sending a message to the past could do it it were possible, unless we're in the whole branching worlds simulation. Jachra 06:34, 5 September 2007 (UTC)

[edit] Poe's entanglement

The first mention of entanglement in literature was made by Edgar Allan Poe in his November 1838 short story A Predicament. In it, the protagonist manages to have her head stuck in a church steeple's large clock face, with the sharp minute hand slicing her neck.

My eyes, from the cruel pressure of the machine, were absolutely starting from their sockets. While I was thinking how I should possibly manage without them, one actually tumbled out of my head, and, rolling down the steep side of the steeple, lodged in a rain gutter which ran along the eaves of the main building. The loss of the eye was not so much as the insolent air of independence and contempt with which it regarded me after it was out. There it lay in the gutter just under my nose, and the airs it gave itself would have been ridiculous had they not been disgusting. Such a winking and blinking were never before seen. This behaviour on the part of my eye in the gutter was not only irritating on account of its manifest insolence and shameful ingratitude, but was also exceedingly inconvenient on account of the sympathy which always exists between two eyes of the same head, however far apart. I was forced, in a manner, to wink and blink, whether I would or not, in exact concert with the scoundrelly thing that lay just under my nose.

Here, two unattached objects (eyes) act together while being separated by a distance, without regard to the position of the observer. This merits inclusion in the Quantum entanglement article, as both are products of the human imagination.Lestrade 19:29, 22 August 2007 (UTC)Lestrade

Although interesting - I don't really think this is appropriate to include in an article about 'quantum' entanglement. PhySusie (talk) 16:59, 17 January 2008 (UTC)

[edit] Why tensor product?

In section Pure States:

Consider two noninteracting systems A and B, with respective Hilbert spaces HA and HB. The Hilbert space of the composite system is the tensor product
H_A \otimes H_B .

My questions are:

1. Why the composite Hilbert space is from tensor product H_A \otimes H_B ., but not cartesian product H_A \times H_B .?
2. Is the tensor product a consequence which can be derived from Schrodinger equation?

Thank you!

Justin545 (talk) 00:26, 26 January 2008 (UTC)

[edit] Composite System and Tensor Product

It always be true the tensor product is accounted for the concept of composite quantum systems, quantum entanglement especially. As well, it is a big deal with respect to quantum computation. The massive Hilbert space of the composite system dramatically boosts the power of quantum computers. According to postulate of quantum mechanics, the Hilbert space of a composite system is the Hilbert space tensor product of the state spaces associated with the subsystems. But it's rare to see any article which can point out where such a postulate comes from. Is the postulate due to the overwhelming, experimental evidence? Is it a derivational consequence from fundamental quantum theory?

It's difficult to convince me of the ability and the power of quantum computation if no one can tell how the composite quantum system relates to the tensor product. Hopefully, the postulate came from the derivational consequence of quantum theory rather than just from the experimental evidence. After reviewed the original EPR paper, I came up with an idea. So I tried to explain it myself. Although the explanation is very likely to be wrong and even seems naive and optimistic, I would like to put it here to see if anyone could give some advice or correction to my faults. For simplicity, the following assumes all relevant state spaces are finite dimensional.

For a composite system of two particles, the wave function is

Ψ(x1,x2) 

 

 (1)

 

where x1 and x2 are respective positions of the first and the second particles. Similar to the way Separation of variables for solving PDE, if the wave function can be separated into multiplication of two functions such that

Ψ(x1,x2) = U(x1)V(x2) 

 

 (2)

 

As a result, the functions U(x1) and V(x2) can be viewed as wave functions for the first and the second particles, respectively. Furthermore, U(x1) and V(x2) are in Hilbert spaces HA and HB, respectively. Therefore, the two functions can be expanded by their related basis such that

U(x_1)=\sum_i a_i |i\rangle_A 

 

 (3)

 

V(x_2)=\sum_j b_j |j\rangle_B 

 

 (4)

 

where \{|i\rangle_A\} and \{|j\rangle_B\} are respective sets of basis for HA and HB. Substitute (3) and (4) into (2), we have

\Psi(x_1,x_2)=\left(\sum_i a_i |i\rangle_A\right) \left(\sum_j b_j |j\rangle_B\right)

=\left(a_1 |1\rangle_A + a_2 |2\rangle_A + ... + a_m |m\rangle_A\right) \left(b_1 |1\rangle_B + b_2 |2\rangle_B + ... + b_n |n\rangle_B\right)

=\sum_{i,j} a_ib_j|i\rangle_A |j\rangle_B 

 

 (5)

 

Since |i\rangle_A and |j\rangle_B are in different Hilber spaces, their multiplication is equivalent to their tensor product. Thus

|i\rangle_A|j\rangle_B=|i\rangle_A \otimes |j\rangle_B 

 

 (6)

 

Substitute (6) into (5), we have

\Psi(x_1,x_2)=\sum_{i,j} a_ib_j \left(|i\rangle_A \otimes |j\rangle_B\right) =\sum_{i,j} a_ib_j |ij\rangle_{AB} 

 

 (7)

 

That (7) is a state or vector in Hilber space H_A \otimes H_B. And (7) can be generalized to systems that involve more than two particles or subsystems. However, it is problematic such as

  1. The method of the separation of variables can not guarantees to be the solution for every class of PDE. Likewise, not all wave function of form (1) can be separated into multiplication of two functions of form (2).
  2. Even if the wave function (1) could be separated to the form of (2) "mathematically", but does it make physical sense to say that the functions U(x1) and V(x2) are two "wave functions" which are the component systems of Ψ(x1,x2)?

Well, I am neither a mathematician nor a physicist. I don't mean to offend or mislead someone with my words. I am just hoping to get more clue by this discussion.

Justin545 (talk) 10:12, 22 February 2008 (UTC)

[edit] minor change

I just added "in general" to the sentence "is impossible, in general, to predict, according to quantum mechanics, which set of measurements will be observed", in the introductory section. This is because if a system is in the eigenstate of an observable, then the quantum mechanics postulates allow to predict the result of a measurement. Oakwood (talk) 00:02, 6 March 2008 (UTC)

[edit] Some questions

I would like to ask the august people present here some questions? I remember that string theory supposes that there are additional dimensions to our familiar three, yet that those are collapsed in a point.

A point is a mathematical idea that was long borrowed by physicists to simplify some calculations. One of the speculations introduced by quantum theory is that there is a limit to how small anything could be. There being a dimension assumes that there can be movements and measurements in that dimension. If you can find Flatland or George Gamow's One, Two, Three... Infinity, you can see discussions of what life would be like for a two-dimensional creature.
The question that people have asked string theorists is why, if there are more than four dimensions, there are no signs of movement or difference of locations in those additional dimensions. One answer proposed is that the dimensions might be so limited in extent that they would approximate a point, i.e., they might be so limited that it would be virtually impossible to measure them. If you and I started out side by side a mile from the Washington Monument, and then I climbed a long ladder 90 degrees doon in the fifth dimension and made the same measurement then I ought to find a slightly longer distance to the monument since I would be measuring the hypotenuse of a right triangle while you would be measuring the long leg of the same triangle. But if my ladder could only be an inch long then it would be hard to discover any difference in length experimentally.P0M (talk) 01:42, 14 May 2008 (UTC)
Thank's for the input. I´ll try not to sound very stupit, but why would we be able to discern the precense of additional spatial dimensions? If we think about the classical two dimensional creatures, how would they notice the precense of a three dimensional being or precense in they´r wiscinity? Say a person, i.e. one of us, would be standing on a flat plane, a two dimensional being would only perceive a two dimensional outline of the bottom of our feet, presumably. If we would be walking, we might to theyr perceptions appear,,,that is the tiny aspect of us they´d be able to perceive...to apparate and disapparate so to speak without regard to the rules in which they were used to things and familiar phenomena to be operating under. Tink about it, a line in theyr path would be an obstackle for them, which they would need to get around, while we would simply step over thus to them appear to disappear and then appearing where to them it would seem illogical for us to be appearing. Wouldn´t a two dimensional being be quite incapable of perceiving additional spatial dimensions, and might the same not hold for us? What I´m implying is that additional phenomena might be all around us without us being able to perceive them except in a very hapsard manner...somewhat in the manner of the inability of a two dimensional being to oberve how logical walking is for us. It would be very easy for us to stand abow theyr plane and thus to be completelly unobservable for them. Perhaps four or even five dimensional precenses or beings can do similar to us, perhaps they are.
One of the things that makes us believe that three spatial dimensions may not be enough to explain everything is that the Universe seems to be expanding, but it is not growing "at the edges." Every thing is getting farther away from every other thing. Imagine that our two dimensional creatures were on a balloon that was slowly expanding, but that the "planets" on this sphere were more like solid buttons. The buttons would stay the same size, but the distances between them would increase.
Indeed, the rational mind insists the universe must be inflating into something. That it must be a part of something waster, in some manner.
One way that a two-dimensional creature might decide that something odd was going on would be that, if s/he lived on a spherical surface the angles of a triangle would equal 180 over small distances, but would equal more than 180 degrees if, e.g., the triangle had its bottom formed by the equator and its two sides met at the north pole.
We can hope that means can be found to indirectly confirm the existence of additional dimensions.
Some people think that there may be more than three dimensions and that we may move in all of them, but say that if the possible range of travel in the additional dimensions is very small you would not expect to be able to notice. All that they are saying is that maybe there is something to look for, reason to think that mathematical ideas and string theories may not be fantasy, etc. P0M (talk) 07:47, 15 May 2008 (UTC)
I understand that mathematicians have created mathematical descriptions of four dimensional shapes. That may give grounds to hope, as mathematics frequently are decates ahead of technological trends, that technological means may eventually be discovered to confirm the existence of additional dimensions all around us.

There also does exist brane theory, which proposes that brains moving through some additional spatial dimension are causing our universe, or other universes as well, to come into being as they move about through that additonal dimension every now and a then touching. Now, if we can accept the presence of additional dimensions,the question might be quite relevant how that affects quantum systems.

This view is highly speculative. Can you document its source?P0M (talk) 01:42, 14 May 2008 (UTC)
Please excuse that I don´t have a book to go by, but this [2] is one of the linked articles available discussing it in a language the public can understand.

I)Might particles actually be moving in more dimensions than three, hence their movements being potentially fully measurable and predictable in four or more dimensions?

We already know that particles (and everything else) move in four dimensions, and that what we really have to measure is the movement of things in space and time if we are not going to have trouble understanding things like time dilation. The same reasoning would apply to movement in more dimensions. If we had some way of affecting a photon so that its speed from point A to point B was different from an un-messed-with photon traveling from point A to point B, then we might suspect that unbeknownst to us it was following a different path. A two-dimensional creature on the surface of a sphere might shoot off a photon that would follow the surface of the sphere and travel a great circle path from A to B at the speed c, and the somehow shoot off another photon that would go through the sphere (assuming it to be transparent of course) and get there in a shorter time. "Old fashioned" science fiction spoke of warping space to accomplish the same feat in our universe. P0M (talk) 01:42, 14 May 2008 (UTC)
Clearly I was talking about spatial dimensions. But think about a three dimensional person walking over a plane populated by two dimensional beings. Two dimensional beings are presumably used to the need to circumnavigate lines that obstruct theyr path, while to us such a line might only be a slight obstruction that can be overstepped, climbed over or othervice overcome beyond the sight of the two dimensional beings. To them, as we are appearing/disappearing to theyr sences not according to any rules they are familiar with, our path might seem wholly random as aspects of our path are invisible to them, while to our three dimensional perceptions our path is wholly logical and reasonable as we are unlike them able to perceive all of it but they only the aspects of our path which touches theyr plane. This is more in the way of the kind of analogy I´m talking about. The suggestion is that a particle may, if it´s movements in additional spatial dimensions can be accounted for, in fact be wholly predictable in its movements even though to our three dimensional perception capabilities its movements appear wholly random as there are aspect of its path we simply are not equipped to perceive. In other words that the randomness is only an illution due to our limited perception capabilites.

In other words might the presence of uncertainty only be due to our inability to measure their states through additional spatial dimensions? This assumes that higher spatial dimensions are not in a collapsed state.

I don't see how that is going to work. Using the above analogy, suppose that the two-dimensional creature didn't have good control of which path his photons would take. Then there would be uncertainty in how long a light signal would take. It would really mess up their physics because from their original naive point of view the speed of light would be different on different occasions. For all they knew the variations in the speed of light might be analogous to the variations in the speeds of horses or racing pigeons. P0M (talk) 01:42, 14 May 2008 (UTC)
I prefer the analogy of a three dimensional being walking across a plane populated with two dimensional beings. In the case of the light, the two dimensional being would only perceive some of the light being emitted. For all what we know a light cone is only the three dimensional wisible part. As far as I can see, as the two dimensional beings are unable ot observe a three dimensional light cone, just as well would we be unable to observe if a lightcone has a shape in an additional spatial dimension.
Of course all of this stuff is speculative. The Flatland discussions are intended to help us imagine how things could operate in higher dimensions. String theory is perhaps the first place where multiple higher dimensions may have real significance. If we really are in a Universe of many dimensions we may find ourselves stymied in investigating it very detailed ways unless we find ways to operate outside our own dimension. How could a two dimensional creature fire something into the third dimension? It's pretty hard to see a direct way. Suppose that a two-dimensional creature lived on a flat two-dimensional surface but managed, somehow, to do something like drawing a circle on that space and then causing the area within the circle to increase in area without permitting the circumference to increase. The only way that could happen would be for the surface to bulge into the third dimension. Any creature within the circle might notice that triangles no longer had a sum of 180 degrees or other such phenomena.
As we appear to be able to mathematically decripe some four dimensional shapes, that perhaps indicates that in the future it may become possible to create a device to observe in an additional dimension. Perhaps that´s all it would take, i.e. travel into a fourth dimension wouldn´t be necessary. Apparently dark matter is all around us. As far as we can tell, it forms no objects that can be observed. Maybe, the precense of dark matter is another indirect indication of the precense of additional dimensions as after all if matter of some kind has formed objects/structures that manifest only from a perspective of more than three dimensions, they presumably as a result would be pretty much invisible to our current means of observation with the sole exception of gravitical influences.
I'm not sure what this discussion has to do with entanglement. The entanglement phenomena seem to take place without anything traveling (or with something traveling at infinite speed), rather than something getting from place to place sooner than expected due to having gone through some kind of space warp. Discussion of entanglement put into question our assumptions about locality both in space and in time. Things that are "located in different places" and that are "located at different times" may interact. P0M (talk) 07:47, 15 May 2008 (UTC)
Hmm, think of it as establishing the groundwork. I think that additional dimensions are needed to explain entanglement. If for the sake of argument we accept the precense of additional dimensions, i.e. the 4th., 5th. and so on, and moreover that matter propably exists in those additional dimensions which only manifests to our observations so far through gravitational influences, that for one might explain why this dark matter interacts litle with our familiar matter as it may simply be moving around the three dimensional solids we are familiar with through an additional dimension of travel. If matter exists in those dimensions, it means particles exist there and probably that familiar particles interact with those dimensions as well...meaning that they move presumably also in a fourth dimension as well as our familiar three, and perhaps even more dimensions. Now, in the case of entanglement, I wonder if that phenomena may not even involve a 5th. dimension. I suggested earlier that if our universe may appear to be a three dimensional brane from a fourth dimensional perspective, it may even appear as simply a point from a fifth dimensional perspective meaning that through a fifth dimensional perspective all points within our own might be in the same place so to speak...remember that one dimension down from our perspective is flatland and two dimensions down from our perspective is a point. My thinking is that entanglement works in the way that the entagled particles essentially become one,i.e. that they have effectivelly become a single particle, being connected through a 5th. dimension where all points within our universe are together in one. That would explain the apparent instantaneous effect independent seeming from our observed distance. Hmm, I wonder what that would affect the 'no-cloning theorem.' According to my idea passing information independent of distance observed to us through the means of entanglement would neither be 'transmission' nor would it either be 'cloning' as no copy would be made of a particle, rather two particles would become one so that observed condition of the said particle at what to us appears to be the one end would inevitably be the same at the other. Whichever party would make the observation would decide the state of the merged particle.

II)Alternativelly, if higher dimensions are collapsed in a point, truly, from our perspective, might that be different from the perspective of a higher dimension? In other words might our universe be only a single point from the perspective of a higher dimension?

A straight line, no matter how long, looks like a point when seen from right on. But the logic of the situation means that it is in the lower dimensions that tesseracts get compressed into cubes within cubes, that cubes get compressed into squares within squares with their vertices connected, and that squares get compressed into single lines or one or two points. (Make a square out of soda straws and light it from inside and outside and then watch the shadows you can create.) P0M (talk) 01:42, 14 May 2008 (UTC)
It´s indeed a touchy, but how would our universe appear from a 4 dimensional perspective or 5 dimensional perspective. I have read the idea that from a 4 dimensional perspective our universe might appear to be a brane and moreover that there may be more such even infinite numbers.

That proposes the idea, that if a higher dimension is a factor in the movements of quantum particles, then by moving in that they may appear in different places within our universe without actually being traveling across the apparent to us spatial distance somewhat like they were traveling through a wormhole, say if we are a dot to the perspective of the higher dimension...then perhaps all dots within our universe touch that same dot in the higher dimension. Perhaps then superluminal communication to our appearance wouldn´t actually be superluminal as the particles wouldn´t be moving in three dimensional space through that distance. Is this just insane rambling?

One of the ideas that you seem to be circling around, and one that has to do with string theory, is that what kind of fundamental particle is observed depends on how a single string is vibrating. If you only have two dimensions (plus time) to move around in there are very limited ways that a "string" (actually a line in this case) could vibrate. If you have three dimensions then the dancing string can be more athletic. It can go upstage and downstage as well as going side to side and up and down. But I think the string theorists were not able to come up with enough vibrational forms that way, so they asked how many dimensions would be required to form a coherent theory that would account for the phenomena that are here to be observed. So we could see something as "just a point" that was enthusiastically bopping back and forth along a line in the Nth dimension, just as a two-dimensional creature could see a sewing needle poking in and out of the membrane he lived on as a motionless little circle. P0M (talk) 01:42, 14 May 2008 (UTC)

—Preceding unsigned comment added by 194.144.20.188 (talk) 00:26, 14 May 2008 (UTC)

Yes, that is the general idea. I´ve been wondering wether there aren´t actually 4 dimensional precenses around us. Think about it, how would they appear to us. Wouldn´t we only be able to perceive them very fleetingly, and apparently quite randomly, somewhat in the manner of a two dimensional creature to which our appearances would indeed appear very fleeting, random and outside the rules of behavour they´re use to. If there are four dimensional appearances randomly, as far as we can perceive them, appearing/disappearing, without behaving in a way that appears reasonable to our standards...wouldn´t most of us simply think it an illusion and clean reject the whole idea?
Here is a thought experiment that may further your thinking about dimensions and physical changes. I'll leave working out the experimental details to others. Suppose that you have a rotating disk. It happens to be rotating clockwise. Its axle is attached to the wall of a transparent cylinder that is about as wide as the disk's diameter. Next you perform the following operation: You rotate the cylinder half a turn in either direction, d=½. Now the disk is pointing away from you, and you perceive it as spinning counter-clockwise. To restore its original spinning mode (from your point of view), you perform that operation a second time, d=1. Each of those operations is equivalent to flipping a spinning top. Next you replace the ordinary cylinder with a Möbius strip. (Make a long strip of paper, give it half a twist, and paste the ends together.) When you rotate this modified holder the full distance, d=1, as you rotated the original cylinder to get its original spin back, you will find that you have changed the spin from clockwise to counter-clockwise. So to get the original spin orientation back, you have to perform the same operation four times rather than twice. Even more unexpectedly, if you view it at its near and far locations, equivalent to flipping the top, you will see the sequence cw, ccw, ccw, and cw. If it were an apparently regular top and it happened to be spinning clockwise before you flipped it the first time, you would fine it spinning counter-clockwise the next time. O.K. so far, so you flip it again, and it is still spinning counter-clockwise. Then you flip it a third time, and this time it seems to meet your normal expectations and it comes up spinning clockwise again. Maybe you would go away satisfied that you had just failed to flip it the second time you tried... but then you try it again. The Möbius strip is a curiosity because both sides are the same side. There is a three-dimensional analog called a Klein's bottle. Do not store your wine in a Klein's bottle. It may turn hallucinogenic. ;-) P0M (talk) 03:01, 14 May 2008 (UTC)

This section seems to be something stuck in by the writer without regard to context. Probably it should have been put in at the bottom of the page. P0M (talk) 03:01, 14 May 2008 (UTC)