Entanglement in fermion systems

dc.creatorGigena, Nicolás Alejandro
dc.creatorRossignoli, Raúl Dante
dc.date2015-10
dc.date.accessioned2023-08-31T00:29:32Z
dc.date.available2023-08-31T00:29:32Z
dc.identifierhttp://hdl.handle.net/11336/181412
dc.identifierGigena, Nicolás Alejandro; Rossignoli, Raúl Dante; Entanglement in fermion systems; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 92; 4; 10-2015; 423261-423269
dc.identifier1050-2947
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8543479
dc.descriptionWe analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with a fixed number parity yet not necessarily a fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert space H is defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases of H is a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined by J. Schliemann et al. [Phys. Rev. A 64, 022303 (2001)PLRAAN1050-294710.1103/PhysRevA.64.022303], implying that particle entanglement may be seen as minimum mode entanglement. It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that in the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy is evaluated analytically, extending the results in previous reference to general states.
dc.descriptionFil: Gigena, Nicolás Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
dc.descriptionFil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
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dc.languageeng
dc.publisherAmerican Physical Society
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.92.042326
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.042326
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1509.05970v2
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subjectEntanglement
dc.subjectFermionic Systems
dc.subjecthttps://purl.org/becyt/ford/1.3
dc.subjecthttps://purl.org/becyt/ford/1
dc.titleEntanglement in fermion systems
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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