Entanglement at finite temperatures in the electronic two-particle interferometer

In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers (2PIs) at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group (Neder et al 2007 Nature 448 333) realizing the two particle interferometer proposed by Samuelsson et al (2004 Phys. Rev. Lett. 92 026805). The experiment displayed a clear two-particle Aharonov-Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. This raised qualitative as well quantitative questions about entanglement production and detection in mesoscopic conductors at finite temperature. As a response to these questions, in our recent work (Samuelsson et al 2009 Phys. Rev. Lett. 102 106804), we presented a general theory for finite temperature entanglement in mesoscopic conductors. Applied to the 2PI we showed that the emitted two-particle state in the experiment was clearly entangled. Moreover, we demonstrated that the entanglement of the reduced two-particle state, reconstructed from measurements of average currents and current cross correlations, constitutes a lower bound to the entanglement of the emitted state. The present work provides an extended and more detailed discussion of these findings.