Entropic relations for indistinguishable quantum particles

• URL: http://arxiv.org/abs/1702.02360v2
• Date: Mon, 16 Dec 2024 14:59:37 GMT
• Title: Entropic relations for indistinguishable quantum particles
• Authors: Marius Lemm,
• Abstract summary: The von Neumann entropy of a $k$-body reduced density matrix $gamma_k$ quantifies the entanglement between $k$ quantum particles and the remaining ones. The results hold for indistinguishable quantum particles and are independent of the statistics.
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• 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.

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