Lower bound for electron spin entanglement from beamsplitter current correlations

TL;DR

This paper establishes a practical lower bound for electron spin entanglement in mesoscopic conductors using current correlation measurements, accounting for decoherence and thermal effects, and enabling entanglement quantification in experimental setups.

Contribution

It introduces a method to estimate a lower bound of electron spin entanglement from measurable current correlations, including effects of relaxation and decoherence during transmission.

Findings

Lower bound for entanglement expressed via current correlators.

Quantification of entanglement reduction due to thermal mixing.

Method to determine entanglement, relaxation, and decoherence times experimentally.

Abstract

We determine a lower bound for the entanglement of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross-correlators) after transmission through an electronic beam splitter. The effect of spin relaxation (T_1 processes) and decoherence (T_2 processes) during the ballistic coherent transmission of the carriers in the wires is taken into account within Bloch theory. The presence of a variable inhomogeneous magnetic field allows the determination of a useful lower bound for the entanglement of arbitrary entangled states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and the relaxation (T_1) and decoherence (T_2) times can be determined.