Proposal for production and detection of entangled electron-hole pairs in a degenerate electron gas

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(T1T2)(1/2)(T-1+T-2)(-1), with T-1,T-2<1 the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as an experimental realization.