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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.
Marius Lemm (Tue,) studied this question.
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