Appears in collection : Operator Algebras and Quantum Information Theory

Alice and Bob stand for the separated labs scenario, a standard setting for many quantum informational tasks, where two labs are not connected by quantum interactions, but are capable of arbitrary local operations. When “local” is formalized by two commuting von Neumann algebras, as is natural in algebraic quantum field theory, there are characteristic deviations from the case of two (usually even finite) type I algebras, which is almost exclusively studied in quantum information theory. In particular, there is a new kind of connection: It may be impossible to perform “arbitrary local operations” on the subsystems. The prototype of a forbidden operation is complete depolarization, i. e. , destroying one subsystem, and replacing it with a new one in a fixed state. This operation usually has no normal extension to the whole system. It would result in a product state, and there are often no normal ones. Thus the notion of separable states loses its relevance. On the other hand, a von Neumann-algebraic system may be used as an (idealized) infinite resource for entanglement, for which the hyperfinite type II_1 factor is the canonical prototype, or even allow for exact embezzling, for which, similarly, the hyperfinite type III_1 factor is the canonical prototype.