Noise correlations, entanglement, and Bell inequalities

TL;DR

This paper explores how noise correlations can reveal entanglement and Bell inequality violations in electron transport experiments involving superconductors and correlated electron systems.

Contribution

It demonstrates the direct monitoring of noise correlations to identify entanglement in quantum circuits with superconductors and carbon nanotubes.

Findings

Noise correlations can be used to detect entanglement.

Bell inequalities are violated in electron transport experiments.

Entanglement is explicitly illustrated via noise correlations in quantum circuits.

Abstract

The aim of this chapter is to describe two situations where positive noise correlations can be directly monitored using a transport experiment, either with a superconductor or with a correlated electron system. To be more precise, the present text reflects the presentations made by the three authors during the Delft NATO workshop. Bell inequalities and quantum mechanical non-locality with electrons injected from a superconductor will be addressed first. Next, noise correlations will be computed in a carbon nanotube where electrons are injected in the bulk from a STM tip. The first topic is the result of an ongoing collaboration with G. Lesovik and G. Blatter over the years. The unifying theme is that in both branched quantum circuits, entanglement is explicit and can be illustrated via noise correlations. Entanglement can be achieved either for pairs of electrons in the case of superconductor sources connected to Fermi liquid leads, or alternatively for pairs of quasiparticle excitations of the correlated electron fluid.