Hybrid Quantum Systems: Complementarity of Quantum Privacy and Error-Correction, and Higher Rank Matricial Ranges

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Date

2019

Authors

Nelson, Mike Ignatius

Journal Title

Journal ISSN

Volume Title

Publisher

University of Guelph

Abstract

We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive dimension inequalities on the associated operator algebras that further quantify the trade-off between correction and privacy.

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Keywords

Quantum Channel, Complementary maps, Operator algebras, Private quantum codes, Private algebras, Correctable algebras, Multiplicative domains

Citation

David W Kribs, Jeremy Levick, Mike I Nelson, Rajesh Pereira, and Mizanur Rahaman. Quantum complementarity and operator structures. Quantum Information & Computation, 19:67�??83, 2019, https://doi.org/10.26421/QIC19.1-2-5