Entropic relations for indistinguishable quantum particles

Abstract

The von Neumann entropy of a $k$-body reduced density matrix ${\hat{I}}_k^3$ quantifies the entanglement between $k$ quantum particles and the remaining ones. In this short paper, we rigorously prove general properties of this entanglement entropy as a function of $k$: it is concave for all $1\le k\le N$ and non-decreasing until the midpoint $k\le \lfloor N/2\rfloor$. The results hold for indistinguishable quantum particles and are independent of the statistics.

8 pages; revised published version with different title, but same results