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4 May 2012 Probability density function for representing quantum states of polarized optical field in the basis of linearly polarized photons
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Abstract
In this paper authors discuss the inverse problem for the density operator describing a bi-modal quantum mixed states of polarized optical field with the reduced probability density function. It is reduced because we assume that photons phase is known - it is represented by the Dirac delta function in the probability distribution. We ask for example if it is possible to represent an elliptically polarized plane wave in the basis of linearly polarized photons (or photons with any other arbitrary chosen phase). Our goal is to define a reversible integral transformation in order to represent the reduced probability density function by the density operator describing a mixed state and to analyze the uniqueness of the solution. This problem is similar to calculating Glauber-Sudarshan function when representing a quantum mixed state in the coherent states basis. However the integral transformation that we search is not that easy to define. It is based on convolution and cross-correlation operations. The operator that generates this transformation is defined using the Stokes operators.
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Lukasz Michalik and Andrzej W. Domanski "Probability density function for representing quantum states of polarized optical field in the basis of linearly polarized photons", Proc. SPIE 8440, Quantum Optics II, 84400S (4 May 2012); https://doi.org/10.1117/12.922207
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