Entanglement witnessing and quantum cryptography with non-ideal ferromagnetic detectors

Abstract

We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $\eta >1/\sqrt{3}\approx 58$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $\eta >1/\sqrt[4]{2}\approx 84$. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

10 pages, 4 figures

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