Reduced and projected two-particle entanglement at finite temperatures.

We present a theory for two-particle entanglement production and detection in mesoscopic conductors at finite temperature. The entanglement of the density matrix projected out of the emitted many-body state differs from the entanglement of the reduced density matrix, detectable by current correlation measurements. Under general conditions reduced entanglement constitutes a witness for projected entanglement. Applied to the recent experiment [Neder et al., Nature (London) 448, 333 (2007)10.1038/nature05955] on a fermionic Hanbury Brown Twiss two-particle interferometer we find that despite an appreciable entanglement production in the experiment, the detectable entanglement is close to zero