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Lectures on Quantum Optics and Quantum Information

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The Wigner Functi<strong>on</strong>: Functi<strong>on</strong>:<br />

Negativity<br />

(From A. Ourjoumtsev PhD Thesis)<br />

Wigner functi<strong>on</strong> of<br />

a single-phot<strong>on</strong><br />

The Wigner functi<strong>on</strong> is a quasi-probability<br />

distributi<strong>on</strong>: it can take negative values.<br />

Huds<strong>on</strong>-Piquet Theorem for pure state:<br />

Gaussian state Positive Wigner functi<strong>on</strong><br />

N<strong>on</strong>-Gaussian state Negative Wigner functi<strong>on</strong><br />

Negativity at the origin, W(0,0)

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