Related papers: Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles

Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles

URL: http://arxiv.org/abs/2401.06917v2
Date: Sat, 14 Sep 2024 15:42:27 GMT
Title: Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
Authors: J. A. Cianciulli, R. Rossignoli, M. Di Tullio, N. Gigena, F. Petrovich,
Abstract summary: We analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions. It leads to exact $(M,N-M)$ Schmidt-like expansions of the state for any $MN$ and is directly related to the isospectral reduced $rho(M)$ and $rho(N-M)$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions, based on $M$- and $(N-M)$-particle states. It leads to exact $(M,N-M)$ Schmidt-like expansions of the state for any $M<N$ and is directly related to the isospectral reduced $M$- and $(N-M)$-body density matrices $\rho^{(M)}$ and $\rho^{(N-M)}$. The formalism also allows for reduced yet still exact Schmidt-like decompositions associated with blocks of these densities, in systems having a fixed fraction of the particles in some single particle subspace. Monotonicity of the ensuing $M$-body entanglement under a certain set of quantum operations is also discussed. Illustrative examples in fermionic and bosonic systems with pairing correlations are provided, which show that in the presence of dominant eigenvalues in $\rho^{(M)}$, approximations based on a few terms of the pertinent Schmidt expansion can provide a reliable description of the state. The associated one- and two-body entanglement spectrum and entropies are also analyzed.

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