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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonlocality in the presence of superselection rules

Frank Verstraete, Norbert Schuch, J. I. Cirac

Published May 25, 2004• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.548387

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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.
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.
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.
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.
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.
Super-selection rules severely restrict the possible operations one can perform on an entangled state. Their effect on the observation of non-locality through the Bell inequalities is only partially understood in the bipartite case. In this article we examine a range of multipartite entangled states and find that for those states the super-selection rules limit the genuinely multipartite nonlocality but not the non-genuinely multipartite. We argue that when the number of particles is smaller than the number of parties, genuinely multipartite nonlocality cannot be detected unless the super-selection rules can be relaxed. The tests proposed in the paper can be implemented using routinely used experimental techniques.
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.