Exact relations between particle fluctuations and entanglement in Fermi gases
Dipartimento di Fisica dell'Università di Pisa and INFN - Pisa, Italy, EU
Accepted: 26 March 2012
We derive exact relations between the Rényi entanglement entropies and the particle-number fluctuations of (connected and disjoint) spatial regions in systems of N non-interacting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.
PACS: 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 05.30.Fk – Fermion systems and electron gas / 03.67.Mn – Entanglement measures, witnesses, and other characterizations
© EPLA, 2012