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Quantum entanglement theory in the presence of superselection rules

Norbert Schuch·Frank Verstraete·J. Ignacio Cirac
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Abstract

Superselection rules severly 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), quant-ph/0310124] we showed that this resource can be quantified by a single additional number, the superselection induced variance (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 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.

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Norbert Schuch, Frank Verstraete, J. Ignacio Cirac. 2004-04-13. Quantum entanglement theory in the presence of superselection rules. https://doi.org/10.1103/physreva.70.042310

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