Eur. Phys. J. B (2017) 90: 232
https://doi.org/10.1140/epjb/e2017-80033-8

Regular Article

Entanglement distribution statistic in Andreev billiards

¹ Departamento de Física, Universidade Federal da Paraíba, 58297-000 João Pessoa, Paraíba, Brazil
² Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil

^a e-mail: jorgegabrielramos@gmail.com

Received: 13 January 2017
Published online: 27 November 2017

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.