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arXiv:1809.00407

Entanglement Measure of the planar-transverse classical light field

Sun-Hyun Youn

Published Sep 2, 2018• 0 citations
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Abstract

Classical light fields are considered physical examples of nonquantum entanglement\cite{Eberly2011}. We apply concurrence and Schmidt approach to evaluate the degree of entanglement for a generalized polarization state that Qian and Eberly suggested, and we obtained an analytic form of the general entanglement state for planar polarization states of classical light.

DOI
10.48550/arxiv.1809.00407

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Classical light fields are considered physical examples of nonquantum entanglement\cite{Eberly2011}. We apply concurrence and Schmidt approach to evaluate the degree of entanglement for a generalized polarization state that Qian and Eberly suggested, and we obtained an analytic form of the general entanglement state for planar polarization states of classical light.
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Classical entanglement refers to non-separable correlations between the polarization direction and the polarization amplitude of a light field. The degree of entanglement is quantified by the Schmidt number, taking the value of unity for a separable state and two for a maximally entangled state. We propose two detection methods to determine this number based on the distinguishable patterns of interference between four light sources derived from the unknown laser beam to be detected. The second method, being a modification of the first one, has interference fringes with discernable angles uniquely related to the entangled state. The maximally entangled state corresponds to fringes symmetric about the diagonal axis at either a 45° or a 135° direction, while the separable state corresponds to fringes symmetric about either the X or Y axis, or both simultaneously. States with Schmidt number between unity and two have fringes of symmetric angles between these two extremes. We believe these detection methods would be beneficial in both computation and communications applications of the classically entangled states.
In a general form, three-photon polarization states are superpositions of contributions from four three-photon polarization modes with four arbitrary complex coefficients. Entanglement of such states is defined as entanglement between their one-photon and two-photon parts. The degree of entanglement is found explicitly in terms of such entanglement quantifiers as the generalized concurrence, entropy of reduced states and the Schmidt parameter. Polarization Stokes vectors, as well as the Schmidt decompositions of three-photon states are found and discussed. Similarity and differences with respect to biphoton polarization states are discussed too.
We consider polarization states of three photons, propagating collinearly and having equal given frequencies but with arbitrary distributed horizontal or vertical polarizations of photons. A general form of such states is a superposition of four basic three-photon polarization modes, to be referred to as the three-photon polarization ququarts (TPPQ). All such states can be considered as consisting of one- and two-photon parts, which can be entangled with each other. The degrees of entanglement and polarization, as well as the Schmidt decomposition and Stokes vectors of TPPQ are found and discussed.