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Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles by Cianciulli, J. A.; Rossignoli, R.; Di Tullio, M.; Gigena, N.; Petrovich, F. is a scholarly article available to read on EtoBox.

What is Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles about?

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.

Author

Cianciulli, J. A.; Rossignoli, R.; Di Tullio, M.; Gigena, N.; Petrovich, F.

Published

2024

Language

EN