Entropic relations for indistinguishable quantum particles

Abstract The von Neumann entropy of a k -body-reduced density matrix γ 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 ⩽ ⌊ N / 2 ⌋ . The results hold for indistinguishable quantum particles and are independent of the statistics.