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Title: Private algebras in quantum information and infinite-dimensional complementarity

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.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6]
  1. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada)
  2. (France)
  3. Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)
  4. (Canada)
  5. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4 (Ireland)
  6. Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN (United Kingdom)
Publication Date:
OSTI Identifier:
22479613
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; QUANTUM INFORMATION; QUANTUM OPERATORS