Special entangled quantum systems and the Freudenthal construction

Péter Vrana, P. Lévay

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plücker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.

Original languageEnglish
Article number285303
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number28
DOIs
Publication statusPublished - 2009

Fingerprint

Entanglement
Quantum Systems
embedding
Communication
communication
Algebra
Jordan Algebra
Jordan
Separability
Invariant Measure
algebra
degrees of freedom
Degree of freedom
Necessary Conditions
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Special entangled quantum systems and the Freudenthal construction. / Vrana, Péter; Lévay, P.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 28, 285303, 2009.

Research output: Contribution to journalArticle

@article{1832fb1444e9475fbb55f01225d10d6e,
title = "Special entangled quantum systems and the Freudenthal construction",
abstract = "We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Pl{\"u}cker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.",
author = "P{\'e}ter Vrana and P. L{\'e}vay",
year = "2009",
doi = "10.1088/1751-8113/42/28/285303",
language = "English",
volume = "42",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "28",

}

TY - JOUR

T1 - Special entangled quantum systems and the Freudenthal construction

AU - Vrana, Péter

AU - Lévay, P.

PY - 2009

Y1 - 2009

N2 - We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plücker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.

AB - We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plücker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.

UR - http://www.scopus.com/inward/record.url?scp=70449509136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449509136&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/28/285303

DO - 10.1088/1751-8113/42/28/285303

M3 - Article

AN - SCOPUS:70449509136

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 28

M1 - 285303

ER -