Many-body entanglement in fermion systems

We discuss a general bipartitelike 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 sam...

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Autores principales: Gigena, Nicolás Alejandro, Di Tullio, Marco, Rossignoli, Raúl Dante
Formato: Articulo
Lenguaje:Inglés
Publicado: 2021
Materias:
Física
Quantum entanglement
Physics
Schmidt decomposition
Bipartite graph
Majorization
State (functional analysis)
Mathematical physics
Fermion
Upper and lower bounds
Entropy (classical thermodynamics)
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/126239
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-126239
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Quantum entanglement
Physics
Schmidt decomposition
Bipartite graph
Majorization
State (functional analysis)
Mathematical physics
Fermion
Upper and lower bounds
Entropy (classical thermodynamics)
spellingShingle Física
Quantum entanglement
Physics
Schmidt decomposition
Bipartite graph
Majorization
State (functional analysis)
Mathematical physics
Fermion
Upper and lower bounds
Entropy (classical thermodynamics)
Gigena, Nicolás Alejandro
Di Tullio, Marco
Rossignoli, Raúl Dante
Many-body entanglement in fermion systems
topic_facet Física
Quantum entanglement
Physics
Schmidt decomposition
Bipartite graph
Majorization
State (functional analysis)
Mathematical physics
Fermion
Upper and lower bounds
Entropy (classical thermodynamics)
description We discuss a general bipartitelike 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 postmeasurement states. Moreover, such entropy is an upper bound to the 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.
format Articulo
Articulo
author Gigena, Nicolás Alejandro
Di Tullio, Marco
Rossignoli, Raúl Dante
author_facet Gigena, Nicolás Alejandro
Di Tullio, Marco
Rossignoli, Raúl Dante
author_sort Gigena, Nicolás Alejandro
title Many-body entanglement in fermion systems
title_short Many-body entanglement in fermion systems
title_full Many-body entanglement in fermion systems
title_fullStr Many-body entanglement in fermion systems
title_full_unstemmed Many-body entanglement in fermion systems
title_sort many-body entanglement in fermion systems
publishDate 2021
url http://sedici.unlp.edu.ar/handle/10915/126239
work_keys_str_mv AT gigenanicolasalejandro manybodyentanglementinfermionsystems
AT ditulliomarco manybodyentanglementinfermionsystems
AT rossignolirauldante manybodyentanglementinfermionsystems
bdutipo_str Repositorios
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