1111.4836 (Pasquale Calabrese et al.)

Exact relations between particle fluctuations and entanglement in Fermi
gases    [PDF]

Pasquale Calabrese, Mihail Mintchev, Ettore Vicari

We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting 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 Renyi 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.

View original: http://arxiv.org/abs/1111.4836