Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables

Details Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables

2005-06-13

arxiv.org/abs/quant-ph/0506099v1

Physics

Quantum Physics

19 pages, to appear in proceedings of Quantum Structures VII, Int. J. Theor. Phys

Scientific paper

10.1007/s10773-005-8009-z

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones setting, are discussed.

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