Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1005.5407 · Physical Review A

Exchange symmetry and global entanglement and full separability

Tzu-Chieh Wei

Published May 28, 2010• 21 citations
arXivHTMLPDF

Abstract

Ichikawa et al. [Phys. Rev. A 78, 052105 (2008)] showed that exchange symmetry gives rise to a simple characterization of whether multipartite pure quantum states being either globally entangled or fully separable. In this Brief Report, we provide a simple alternative approach and some extension to their conclusions.
DOI
10.1103/physreva.81.054102

Related papers

Exchange symmetry and multipartite entanglement

Tsubasa Ichikawa, Toshihiko Sasaki, Izumi Tsutsui +1 more

Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group ${S}_{N}$. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that antisymmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group ${B}_{N}$ must also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.

arXiv:0805.3625•Physical Review A•Nov 6, 2008•42 citations

Global entanglement for multipartite quantum states

Chang‐shui Yu, He‐Shan Song

Based on the residual entanglement [Phys. Rev. A 71, 042331 (2005)], we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite state. The distinct characteristic of the global entanglement is that it consists of the sum of different entanglement contributions. The measure can provide sufficient and necessary condition of fully separability for pure states and be conveniently extended to mixed states by minimizing the convex hull. To test the sufficiency of the measure for mixed states, we evaluate the global entanglement of bound entangled states. The properties of the measure discussed finally show the global entanglement is an entanglement monotone.

arXiv:quant-ph/0603038•Physical Review A•Feb 15, 2006•33 citations

Detecting genuine multipartite entanglement of pure states with bipartite correlations

Marcin Markiewicz, Wiesław Laskowski, Tomasz Paterek +1 more

Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of $k$ separability.

arXiv:1210.5530•Physical Review A•Mar 26, 2013•26 citations

Chiral Symmetries and Multiparticle Entanglement

Sophia Denker, Satoya Imai, Otfried Gühne

Bosons and fermions are defined by their exchange properties and the underlying symmetries determine the structure of the corresponding state spaces. For two particles there are two possible exchange symmetries, resulting in symmetric or antisymmetric behaviour, but when exploring multiparticle systems also quantum states with chiral symmetries appear. In this work we demonstrate that chiral symmetries lead to extremal forms of quantum entanglement. More precisely, we show that subspaces with this symmetry are highly entangled with respect to the geometric measure of entanglement, leading to observables which can be useful for entanglement characterization. Along the way, we develop a simple method to solve the problem of genuine multiparticle entanglement for unitarily invariant three-particle states and use it to identify genuine multipartite entangled states whose partial transposes with respect to all bipartitions are positive. Finally, we consider generalizations with less symmetry and discuss potential applications.

arXiv:2506.15609•Jun 18, 2025•0 citations

Local unitary equivalence and entanglement of multipartite pure states

Barbara Kraus

The necessary and sufficient conditions for the equivalence of arbitrary $n$-qubit pure quantum states under local unitary (LU) operations derived in [B. Kraus, Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two $n$-qubit states (with $n>2$ arbitrary) which have the properties that all the entropies of any subsystem coincide; however, the states are neither LU equivalent nor can be mapped into each other by general local operations and classical communication.

arXiv:1005.5295•Physical Review A•Sep 30, 2010•85 citations

Quantum coherences of indistinguishable particles

Jan Sperling, Armando Pérez-Leija, Kurt Busch +1 more

We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.

arXiv:1707.05545•Physical Review A•Sep 25, 2017•12 citations
Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group SN{S}_{N}SN​. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that antisymmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group BN{B}_{N}BN​ must also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.
Based on the residual entanglement [Phys. Rev. A 71, 042331 (2005)], we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite state. The distinct characteristic of the global entanglement is that it consists of the sum of different entanglement contributions. The measure can provide sufficient and necessary condition of fully separability for pure states and be conveniently extended to mixed states by minimizing the convex hull. To test the sufficiency of the measure for mixed states, we evaluate the global entanglement of bound entangled states. The properties of the measure discussed finally show the global entanglement is an entanglement monotone.
Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of kkk separability.
Bosons and fermions are defined by their exchange properties and the underlying symmetries determine the structure of the corresponding state spaces. For two particles there are two possible exchange symmetries, resulting in symmetric or antisymmetric behaviour, but when exploring multiparticle systems also quantum states with chiral symmetries appear. In this work we demonstrate that chiral symmetries lead to extremal forms of quantum entanglement. More precisely, we show that subspaces with this symmetry are highly entangled with respect to the geometric measure of entanglement, leading to observables which can be useful for entanglement characterization. Along the way, we develop a simple method to solve the problem of genuine multiparticle entanglement for unitarily invariant three-particle states and use it to identify genuine multipartite entangled states whose partial transposes with respect to all bipartitions are positive. Finally, we consider generalizations with less symmetry and discuss potential applications.
The necessary and sufficient conditions for the equivalence of arbitrary nnn-qubit pure quantum states under local unitary (LU) operations derived in [B. Kraus, Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two nnn-qubit states (with n>2n>2n>2 arbitrary) which have the properties that all the entropies of any subsystem coincide; however, the states are neither LU equivalent nor can be mapped into each other by general local operations and classical communication.
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.