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:quant-ph/0404079 · Physical Review A

Quantum entanglement theory in the presence of superselection rules

Norbert Schuch, Frank Verstraete, J. I. Cirac

Published Oct 15, 2004• 104 citations
arXivHTMLPDF

Abstract

Superselection rules severely constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In Phys. Rev. Lett. 92, 087904 (2004) we showed that this resource can be quantified by a single additional number, the superselection-induced variance $(\mathrm{SIV})$, without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed-state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that $\mathrm{SIV}$ is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.

DOI
10.1103/physreva.70.042310

Related papers

Nonlocal Resources in the Presence of Superselection Rules

Norbert Schuch, Frank Verstraete, J. I. Cirac

Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the superselection induced variance of the local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation, and mixed state entanglement.

arXiv:quant-ph/0310124•Physical Review Letters•Feb 27, 2004•102 citations

Nonlocality in the presence of superselection rules

Frank Verstraete, Norbert Schuch, J. I. Cirac

Effective superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Superselection rules appear in e.g. the context of experiments with entangled cold gases: in this case all local operations have to conserve the local particle number. These superselection rules enforces us to reconsider the notion of nonlocality, as the new constraint implies limitations on the local operations that can be implemented. This gives rise to a novel form of nonlocality, and it is possible to associate a new nonlocal resource to it. In this paper we characterize this new resource, quantify it and discuss some applications.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•1 citation

Entanglement and symmetry: A case study in superselection rules, reference frames, and beyond

S. J. Jones, Howard M. Wiseman, Stephen D. Bartlett +2 more

In recent years it has become apparent that constraints on possible quantum operations, such as those constraints imposed by superselection rules (SSRs), have a profound effect on quantum information theoretic concepts like bipartite entanglement. This paper concentrates on a particular example: the constraint that applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of $N$ Bell-state pairs scaling as $\mathrm{log}(N)$ as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We discuss the apparent disparity with the asymptotic $(N\ensuremath{\rightarrow}\ensuremath{\infty})$ recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be noncollective as well as symmetric. Even under this stronger constraint we, nevertheless, show that Bell nonlocality (and hence entanglement) can be demonstrated for an ensemble of $N$ Bell-state pairs no matter how large $N$ is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].

arXiv:quant-ph/0608056•Physical Review A•Dec 20, 2006•23 citations

Manipulating fermionic mode entanglement in the presence of superselection rules

Ömer Tırınk, Gökhan Torun, Onur Pusuluk

Superselection rules (SSRs), linked to the conservation of physical quantities such as parity or particle number, impose constraints on allowable physical operations in fermionic systems. This affects the amount of extractable mode entanglement possessed in a given state and its manipulation by the so-called entanglement-free operations. Here, we present a majorization-based algorithm for the mixed state transformations of bipartite mode entanglement, where the allowed operations (i.e., resource non-generating operations), that is, local operations and classical communication, are restricted by local SSRs. We then focus on the local parity SSR and investigate the possibility to relax the constraints imposed by it through a catalyst. In particular, we show that an ancillary mode system can catalyze the change in local parity. Finally, we discuss the application of our methodology to various problems in different fields. Accordingly, we propose that it may shed new light on the activation of orbital entanglement in chemical molecules and the manipulation of multipartite entanglement or quantum discord in distinguishable quantum systems.

arXiv:2303.04559•Mar 8, 2023•0 citations

Quantum-nonlocality in the presence of superselection rules and some applications

Frank Verstraete, J. I. Cirac

We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum-nonlocality has to be redefined in the presence of superselection rules: there exist separable states that cannot be prepared locally and exhibit some form of nonlocality. Moreover, the notion of local distinguishability in the presence of classical communication has to be altered. This can be used to perform quantum information tasks that are otherwise impossible. In particular, this leads to the introduction of perfect quantum data hiding protocols, for which quantum communication (eventually in the form of a separable but nonlocal state) is needed to unlock the secret.

•Feb 5, 2003•3 citations

Entanglement Constrained by Superselection Rules

Stephen D. Bartlett, Howard M. Wiseman

Bipartite entanglement may be reduced if there are restrictions on allowed local operations. We introduce the concept of a generalized superselection rule to describe such restrictions, and quantify the entanglement constrained by it. We show that ensemble quantum information processing, where elements in the ensemble are not individually addressable, is subject to the superselection rule associated with the symmetric group (the group of permutations of elements). We prove that even for an ensemble comprising many pairs of qubits, each pair described by a pure Bell state, the entanglement per element constrained by this superselection rule goes to zero for a large number of elements.

arXiv:quant-ph/0303140•Physical Review Letters•Aug 26, 2003•108 citations
Superselection rules severely constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In Phys. Rev. Lett. 92, 087904 (2004) we showed that this resource can be quantified by a single additional number, the superselection-induced variance (SIV)(\mathrm{SIV})(SIV), without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed-state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that SIV\mathrm{SIV}SIV is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.
Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the superselection induced variance of the local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation, and mixed state entanglement.
Effective superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Superselection rules appear in e.g. the context of experiments with entangled cold gases: in this case all local operations have to conserve the local particle number. These superselection rules enforces us to reconsider the notion of nonlocality, as the new constraint implies limitations on the local operations that can be implemented. This gives rise to a novel form of nonlocality, and it is possible to associate a new nonlocal resource to it. In this paper we characterize this new resource, quantify it and discuss some applications.
In recent years it has become apparent that constraints on possible quantum operations, such as those constraints imposed by superselection rules (SSRs), have a profound effect on quantum information theoretic concepts like bipartite entanglement. This paper concentrates on a particular example: the constraint that applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of NNN Bell-state pairs scaling as log(N)\mathrm{log}(N)log(N) as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We discuss the apparent disparity with the asymptotic $(N\ensuremath{\rightarrow}\ensuremath{\infty})$ recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be noncollective as well as symmetric. Even under this stronger constraint we, nevertheless, show that Bell nonlocality (and hence entanglement) can be demonstrated for an ensemble of NNN Bell-state pairs no matter how large NNN is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].
Superselection rules (SSRs), linked to the conservation of physical quantities such as parity or particle number, impose constraints on allowable physical operations in fermionic systems. This affects the amount of extractable mode entanglement possessed in a given state and its manipulation by the so-called entanglement-free operations. Here, we present a majorization-based algorithm for the mixed state transformations of bipartite mode entanglement, where the allowed operations (i.e., resource non-generating operations), that is, local operations and classical communication, are restricted by local SSRs. We then focus on the local parity SSR and investigate the possibility to relax the constraints imposed by it through a catalyst. In particular, we show that an ancillary mode system can catalyze the change in local parity. Finally, we discuss the application of our methodology to various problems in different fields. Accordingly, we propose that it may shed new light on the activation of orbital entanglement in chemical molecules and the manipulation of multipartite entanglement or quantum discord in distinguishable quantum systems.
We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum-nonlocality has to be redefined in the presence of superselection rules: there exist separable states that cannot be prepared locally and exhibit some form of nonlocality. Moreover, the notion of local distinguishability in the presence of classical communication has to be altered. This can be used to perform quantum information tasks that are otherwise impossible. In particular, this leads to the introduction of perfect quantum data hiding protocols, for which quantum communication (eventually in the form of a separable but nonlocal state) is needed to unlock the secret.
Bipartite entanglement may be reduced if there are restrictions on allowed local operations. We introduce the concept of a generalized superselection rule to describe such restrictions, and quantify the entanglement constrained by it. We show that ensemble quantum information processing, where elements in the ensemble are not individually addressable, is subject to the superselection rule associated with the symmetric group (the group of permutations of elements). We prove that even for an ensemble comprising many pairs of qubits, each pair described by a pure Bell state, the entanglement per element constrained by this superselection rule goes to zero for a large number of elements.