Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps

Abstract

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of completely bounded maps, we formulate an algorithm to compute the norm of an arbitrary linear map. We present an implementation of the algorithm via Maple, discuss its efficiency, and consider the case of differences of unitary maps.

21 pages, preprint version

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• Distance measures to compare real and ideal quantum processes
• Group-theoretic algorithms for matrix multiplication
• Dynamics of initially entangled open quantum systems
• Unbounded violation of tripartite Bell inequalities
• Quantum Circuits with Mixed States
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• The maximal p-norm multiplicativity conjecture is false
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Cited by in corpus (6)

• Shorter quantum circuits via single-qubit gate approximation
• Almost all quantum channels are equidistant
• Quantum Query Algorithms are Completely Bounded Forms
• Progress on the Kretschmann-Schlingemann-Werner Conjecture
• Conditions for the approximate correction of algebras
• Purity benchmarking study of error coherence in a single Xmon qubit