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Frontiers in Optics

Wigner distribution: Friend to Biophotonics

Adam P. Wax

Published Jan 1, 2013• 0 citations
Publisher

Abstract

The Wigner distribution provides joint information of a signal in two conjugate domains. Unique insights can be obtained into biophotonics problems by using this formalism to examine the coherence of optical fields.
DOI
10.1364/fio.2013.fw2d.1

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We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the property that the marginals of all linear combinations of the operators coincide with their quantum counterpart. We call it the Wigner distribution, because for position and momentum this property defines the standard Wigner function. In this note we discuss the application to finite dimensional systems, establish many basic properties and illustrate these by examples. The properties include the support, the location of singularities, positivity, the behaviour under symmetry groups, and informational completeness.
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