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Private algebras in quantum information and infinite-dimensional complementarity

2015-11, Crann, Jason, Kribs, David W., Levene, Rupert H., Todorov, Ivan G.

We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.