Fermionic entanglement in superconducting systems

We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic...

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Autores principales: Di Tullio, Marco, Gigena, Nicolás Alejandro, Rossignoli, Raúl Dante
Formato: Articulo
Lenguaje:Inglés
Publicado: 2018
Materias:
Física
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/154209
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062109
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SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-154209
record_format dspace
spelling I19-R120-10915-1542092023-06-12T20:07:14Z http://sedici.unlp.edu.ar/handle/10915/154209 https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062109 issn:2469-9926 Fermionic entanglement in superconducting systems Di Tullio, Marco Gigena, Nicolás Alejandro Rossignoli, Raúl Dante 2018 2023-06-12T14:24:38Z en Física We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed. Quantum Information Research Group Instituto de Física La Plata Articulo Articulo http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
spellingShingle Física
Di Tullio, Marco
Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
Fermionic entanglement in superconducting systems
topic_facet Física
description We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.
format Articulo
Articulo
author Di Tullio, Marco
Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author_facet Di Tullio, Marco
Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author_sort Di Tullio, Marco
title Fermionic entanglement in superconducting systems
title_short Fermionic entanglement in superconducting systems
title_full Fermionic entanglement in superconducting systems
title_fullStr Fermionic entanglement in superconducting systems
title_full_unstemmed Fermionic entanglement in superconducting systems
title_sort fermionic entanglement in superconducting systems
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/154209
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062109
work_keys_str_mv AT ditulliomarco fermionicentanglementinsuperconductingsystems
AT gigenanicolasalejandro fermionicentanglementinsuperconductingsystems
AT rossignolirauldante fermionicentanglementinsuperconductingsystems
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