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 short paper, we rigorously prove general properties of this entanglement entropy as a function of $k$: it is concave for all $1\leq k\leq N$andnon-decreasinguntilthemidpoint$k\leq \lfloor N/2\rfloor$. The results hold for indistinguishable quantum particles and are independent of the statistics.