Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909315658416128 |
|---|---|
| author | Cianciulli, J. A. Rossignoli, R. Di Tullio, M. Gigena, N. Petrovich, F. |
| author_facet | Cianciulli, J. A. Rossignoli, R. Di Tullio, M. Gigena, N. Petrovich, F. |
| contents | 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 $ρ^{(M)}$ and $ρ^{(N-M)}$. 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 $ρ^{(M)}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles Cianciulli, J. A. Rossignoli, R. Di Tullio, M. Gigena, N. Petrovich, F. Quantum Physics 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 $ρ^{(M)}$ and $ρ^{(N-M)}$. 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 $ρ^{(M)}$, 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. |
| title | Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.06917 |