Clauser-Horne inequality and decoherence in mesoscopic conductors

TL;DR

This paper investigates how decoherence affects the violation of the Clauser-Horne inequality in mesoscopic conductors, revealing conditions under which quantum correlations persist despite decoherence.

Contribution

It introduces a model for decoherence in mesoscopic conductors and identifies parameter regimes where CH inequality violation remains robust against strong decoherence.

Findings

Decoherence reduces CH inequality violation but does not eliminate it entirely.

A parameter region exists where violation persists regardless of decoherence strength.

The model uses fictitious leads to phenomenologically simulate decoherence effects.

Abstract

We analyze the effect of decoherence on the violation of the Clauser-Horne (CH) inequality for the full electron counting statistics in a mesoscopic multiterminal conductor. Our setup consists of an entangler that emits a flux of entangled electrons into two conductors characterized by a scattering matrix and subject to decoherence. Loss of phase memory is modeled phenomenologically by introducing fictitious extra leads. The outgoing electrons are detected using spin-sensitive electron counters. Given a certain average number of incoming entangled electrons, the CH inequality is evaluated as a function of the numbers of detected particles and on the various quantities characterizing the scattering matrix. When decoherence is turned on, we show that the amount of violation of the CH inequality is effectively reduced. Interestingly we find that, by adjusting the parameters of the system, there exists a protected region of $Q$ values for which violation holds for arbitrary strong decoherence.