Private quantum channels, conditional expectations, and trace vectors

Authors:
Amber Church;David W. Kribs;Rajesh Pereira;Sarah Plosker
Affiliations:
Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada;Department of Mathematics & Statistics, University of Guelph, Guelph and Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada;Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada;Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada
Venue:
Quantum Information & Computation
Year:
2011

Citing 3
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Abstract

Private quantum channels are the quantum analogue of the classical one-time pad. Conditional expectations and trace vectors are notions that have been part of operator algebra theory for several decades. We show that the theory of conditional expectations and trace vectors is intimately related to that of private quantum channels. Specifically we give a new geometric characterization of single qubit private quantum channels that relies on trace vectors. We further show that trace vectors completely describe the private states for quantum channels that are themselves conditional expectations. We also discuss several examples.