Measurement of classical entanglement using interference fringes

TL;DR

This paper introduces two interference-based detection methods to quantify classical entanglement in light fields, using fringe patterns to determine the Schmidt number and characterize the entangled state.

Contribution

It proposes novel interference fringe techniques to measure the degree of classical entanglement, enabling better transmission channel construction.

Findings

Fringe patterns correlate with the Schmidt number of the classical entangled state.

Maximally entangled states produce fringes symmetric about 45° or 135° axes.

Separable states produce fringes symmetric about X- or Y-axes.

Abstract

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 the interference fringes form discernable angles uniquely related to the entangled state. The maximally entangled state corresponds to fringes symmetric about the diagonal axis at either 45{\deg} or 135{\deg} direction while the separable state corresponds to fringes symmetric either about 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. The detection methods would be beneficial to constructing transmission channels of information contained in the classically entangled states.