Fermionic many-body entanglement is characterized by hypergraph t-designs in small systems, and random large fermionic states concentrate around maximal entanglement according to the trace-fixed Wishart-Laguerre ensemble.
Entropic relations for indistinguishable quantum particles
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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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Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
Fermionic many-body entanglement is characterized by hypergraph t-designs in small systems, and random large fermionic states concentrate around maximal entanglement according to the trace-fixed Wishart-Laguerre ensemble.