Computing stabilized norms for quantum operations via the theory of completely bounded maps

Authors:
Nathaniel Johnston;David W. Kribs;Vern I. Paulsen
Affiliations:
Department of Mathematics & Statistics, University of Guelph Guelph, ON, CANADA;Institute for Quantum Computing, University of Waterloo, Waterloo, ON, CANADA and Department of Mathematics & Statistics, University of Guelph, Guelph, ON, CANADA;Department of Mathematics, University of Houston, Houston, TX
Venue:
Quantum Information & Computation
Year:
2009

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Abstract

The diamond and completely bounded norms for linear maps play an increasingly importantrole in quantum information science, providing fundamental stabilized distancemeasures for differences of quantum operations. We give a brief introduction to thetheory of completely bounded maps. Based on this theory, we formulate an algorithmto compute the norm of an arbitrary linear map. We present an implementation of thealgorithm via MATLAB, discuss its efficiency, and consider the case of differences ofunitary maps.