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New Physics Sae Mulli

Entanglement Measure of the Planar-Transverse Classical Light Field

Sun-Hyun Youn

Published Jan 31, 2019• 0 citations
Publisher

Abstract

Classical light fields are considered physical examples of nonquantum entanglement [1].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
10.3938/npsm.69.97

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Classical light fields are considered physical examples of nonquantum entanglement [1].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.
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.
Nonseparability in classical and quantum states of light gives rise to the notions of classical (local) and quantum (nonlocal) entanglement, usually defined as global features of the fields and states. Here we use concurrence as a measure of this nonseparability and show that it can be spatially resolved, revealing regions of maximum nonseparability and regions with no nonseparability. We use the topical examples of vectorial structured light and its quantum analog, a hybrid spatial mode and polarization entangled states, to test the approach on both local and nonlocal forms of entanglement. Our work has wide reaching implications, for instance, in understanding the spatial dependence of coherence and polarization in vectorial light, as well as in quantum entangled states for imaging, where spatial correlations are vital.
We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.