Spin noise and Bell inequalities in a realistic superconductor-quantum dot entangler

TL;DR

This paper studies how charge and spin current correlations in a superconductor-quantum dot entangler reveal the effects of parasitic channels and spin flips, and evaluates Bell inequality violations as a measure of entanglement fidelity.

Contribution

It provides a comprehensive density matrix analysis of parasitic effects on entangler efficiency and fidelity, and formulates Bell inequality tests based on charge and spin correlations.

Findings

Spin Fano factor is 0 for total noise and -1 for crossed correlations in an ideal case.

Parasitic channels reduce entangler efficiency and fidelity.

Bell inequality violation depends on the measurement time window τ.

Abstract

Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and -1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of non-locality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\tau$. The efficiency of the test is analyzed, comparing $\tau$ to the various time scales in the entangler operation.