Private algebras in quantum information and infinite-dimensional complementarity

Journal Article · Fri Jan 15 00:00:00 EST 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4935399· OSTI ID:22479613

Crann, Jason ^[1]

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1. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada)

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.

• OSTI ID: 22479613
• Journal Information: Journal of Mathematical Physics, Vol. 57, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
QUANTUM INFORMATION
QUANTUM OPERATORS