Entanglement Distribution Statistic in Andreev Billiards

TL;DR

This paper analyzes the statistical distribution of entanglement in Andreev billiards, revealing that such systems always produce non-separable entangled states, supported by analytical and numerical methods.

Contribution

It provides the first detailed statistical analysis of entanglement in Andreev billiards using symmetry classes of scattering matrices, expanding the understanding of entanglement in chaotic mesoscopic systems.

Findings

Entanglement in Andreev billiards always results in non-separable states.

Distribution of concurrence and entanglement of formation are derived analytically.

Numerical simulations confirm the analytical results.

Abstract

We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland-Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation.