Proposal for Production and Detection of Entangled Electron-Hole Pairs in a Degenerate Electron Gas

Abstract

We demonstrate theoretically that the shot noise produced by a tunnel barrier in a two-channel conductor violates a Bell inequality. The nonlocality is shown to originate from entangled electron-hole pairs created by tunneling events—without requiring electron-electron interactions. The degree of entanglement (concurrence) equals $2(T_1{T}_2{)}^{1/2}(T_1+T_2{)}^{-1}$, with $T_1,T_2\ll 1$ the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as an experimental realization.