Many-body entanglement in fermion systems
- URL: http://arxiv.org/abs/2012.13785v2
- Date: Thu, 20 May 2021 18:53:17 GMT
- Title: Many-body entanglement in fermion systems
- Authors: N. Gigena, M. Di Tullio, R. Rossignoli
- Abstract summary: We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions.
The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce a general bipartite-like representation and Schmidt
decomposition of an arbitrary pure state of $N$ indistinguishable fermions,
based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with
the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same
spectrum in such states. The concept of $M$-body entanglement emerges naturally
in this scenario, generalizing that of one-body entanglement. Rigorous
majorization relations satisfied by the normalized $M$-body DM are then
derived, which imply that the associated entropy will not increase, on average,
under a class of operations which have these DMs as post-measurement states.
Moreover, such entropy is an upper bound to the average bipartite entanglement
entropy generated by a class of operations which map the original state to a
bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic
evaluation of the spectrum of $M$-body DMs in some strongly correlated
fermionic states is also provided.
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