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

O. Sauret·T. Martin·D. Feinberg
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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 $τ$. The efficiency of the test is analyzed, comparing $τ$ to the various time scales in the entangler operation.

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O. Sauret, T. Martin, D. Feinberg. 2005-07-12. Spin noise and Bell inequalities in a realistic superconductor-quantum dot entangler. https://doi.org/10.1103/physrevb.72.024544

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