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. In contrast to the zero temperature limit, the entanglement of the density matrix projected out of the emitted many-body state is different from the entanglement of the reduced density matrix, detectable by current correlation measurements. We show that under very general conditions the reduced entanglement constitutes a lower bound for the projected entanglement. Applying the theory to the recent experiment [Neder et al, Nature 448 333 (2007)] 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.