Optimal Entanglement Witness for Cooper Pair Splitters

TL;DR

This paper introduces an optimal entanglement witness for Cooper pair splitters that detects spin-entanglement with only three measurements, simplifying experimental verification of entanglement in solid-state quantum systems.

Contribution

It proposes a novel entanglement witness requiring fewer measurements and identifies optimal settings, advancing experimental detection of entanglement in Cooper pair splitters.

Findings

Entanglement can be detected with moderate decoherence levels.

Optimal measurement settings are identified for the witness.

The method reduces measurement complexity compared to Bell inequality tests.

Abstract

The generation of spin-entangled electrons is an important prerequisite for future solid-state quantum technologies. Cooper pairs in a superconductor can be split into separate electrons in a spin-singlet state, however, detecting their entanglement remains an open experimental challenge. Proposals to detect the entanglement by violating a Bell inequality typically require a large number of current cross-correlation measurements, and not all entangled states can be detected in this way. Here, we instead formulate an entanglement witness that can detect the spin-entanglement using only three cross-correlation measurements of the currents in the outputs of a Cooper pair splitter. We identify the optimal measurement settings for witnessing the entanglement, and we illustrate the use of our entanglement witness with a realistic model of a Cooper pair splitter for which we evaluate the cross-correlations of the output currents. Specifically, we find that the entanglement of the spins can be detected even with a moderate level of decoherence. Our work thereby paves the way for an experimental detection of the entanglement produced by Cooper pair splitters.