Many-body entanglement in fermion systems

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.

arXiv comment13 pages, 1 figure, final version

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Cited by in corpus (6)

• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
• Analyzing the free states of one quantum resource theory as resource states of another
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Degrees of Entanglement in Systems of Three Indistinguishable Bosons: Revisiting the Greenberger-Horne-Zeilinge State
• Analysis of quantum correlations within the ground state of a three level Lipkin model