Entropic relations for indistinguishable quantum particles

TL;DR

This paper establishes fundamental properties of entanglement entropy for indistinguishable quantum particles, showing it is concave and non-decreasing up to the midpoint, regardless of particle statistics.

Contribution

It provides rigorous proofs of the concavity and monotonicity of the von Neumann entropy for reduced density matrices of indistinguishable particles.

Findings

Entanglement entropy is concave in the number of particles.

Entropy is non-decreasing until the midpoint of particles.

Results are independent of particle statistics.

Abstract

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 $1\leq k\leq N$ and non-decreasing until the midpoint $k\leq \lfloor N/2\rfloor$. The results hold for indistinguishable quantum particles and are independent of the statistics.