Entropic relations for indistinguishable quantum particles

The von Neumann entropy of a k-body-reduced density matrix gamma k quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1 <= k <= N and non-decreasing until the midpoint k <=(sic)N/2(sic). The results hold for indistinguishable quantum particles and are independent of the statistics.