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arXiv:cond-mat/0209517 · Springer eBooks

Noise Correlations, Entanglement, and Bell Inequalities

Thierry Martin, Adeline Crépieux C, N. M. Chtchelkatchev

Published Jan 1, 2003• 0 citations
arXivHTMLPDF
DOI
10.1007/978-94-010-0089-5_15

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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 $\ensuremath{-}1$ (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of nonlocality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\ensuremath{\tau}$. The efficiency of the test is analyzed, comparing $\ensuremath{\tau}$ to the various time scales in the entangler operation.