Husimi Q representation

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The Husimi-Q distribution is a mathematical tool used in physics. The Q-representation is a quasi-probability distribution commonly used to represent the quantum state of light. It is used in the field of quantum optics and particularly for tomographic purposes.

[edit] Definition and properties

The Husimi-Q distribution (called Q-function in the context of quantum optics) is the simplest distribution of quasi-probability in phase space. It is defined as

Q(\alpha)=\frac{1}{\pi}\langle\alpha|\rho|\alpha\rangle,

which can be interpreted as π times the probability distribution for the state 'ρ' to be found in the state |\alpha\rangle \langle \alpha | . It can be used to produce a pictorial representation of the state 'ρ' which sometimes make it easier to grasp its properties.

The Q-distribution is normalized to unity,

\int Q(\alpha)\,d\alpha^2 = 1

and is non-negative definite and bounded:

0 \leq Q(\alpha) \leq \frac{1}{\pi}.

[edit] References

  • Ulf Leonhard, Measuring the Quantum State of Light, Cambridge Studies in Modern Optics (1997).
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