Dephasing of entangled electron-hole pairs in a degenerate electron gas

J. L. van Velsen; M. Kindermann; C. W. J. Beenakker

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Dephasing of entangled electron-hole pairs in a degenerate electron gas

J. L. van Velsen·M. Kindermann·C. W. J. Beenakker

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Abstract

A tunnel barrier in a degenerate electron gas was recently discovered as a source of entangled electron-hole pairs. Here, we investigate the loss of entanglement by dephasing. We calculate both the maximal violation E_max of the Bell inequality and the degree of entanglement (concurrence) C. If the initially maximally entangled electron-hole pair is in a Bell state, then the Bell inequality is violated for arbitrary strong dephasing. The same relation E_max=2\sqrt{1+C^{2}} then holds as in the absence of dephasing. More generally, for a maximally entangled superposition of Bell states, the Bell inequality is satisfied for a finite dephasing strength and the entanglement vanishes for somewhat stronger (but still finite) dephasing strength. There is then no one-to-one relation between E_max and C.

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J. L. van Velsen, M. Kindermann, C. W. J. Beenakker. 2003-07-09. Dephasing of entangled electron-hole pairs in a degenerate electron gas. https://arxiv.org/abs/cond-mat/0307198

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