Entanglement in the presence of superselection rules

E. Cattaruzza, E. Gozzi, Carlo Pagani

Norbert Schuch, Frank Verstraete, J. I. Cirac

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.

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.

Stephen D. Bartlett, Howard M. Wiseman, Robert W. Spekkens +1 more

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.

Wayne C. Myrvold