Entanglement at finite temperatures in mesoscopic conductors

We present a theory for two-particle entanglement generation and
detection in mesoscopic conductors at finite temperature. The
entanglement is expressed in terms of the orbital density matrix
reduced from the full many body state emitted by the source. It is
shown that the entanglement decreases with increasing temperature,
reaching zero at a system dependent critical temperature. This is a
consequence of the enhanced fluctuations in the stream of emitted
particles. A Bell inequality and a scheme for quantum state tomography
formulated in terms of current and zero frequency noise is
presented. The relation to the entanglement projected out of the
full many body state is discussed. We apply the
theory to the recent experiment by Neder et al,
Nature '07 on a fermionic two-particle interferometer
and show that a detection of electronic entanglement in mesoscopic
conductors is within experimental reach.