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

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Title: Hybrid Quantum Systems: Complementarity of Quantum Privacy and Error-Correction, and Higher Rank Matricial Ranges
Author: Nelson, Mike Ignatius
Department: Department of Physics
Program: Physics
Advisor: Kribs, DavidBei, Zeng
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.
URI: https://hdl.handle.net/10214/25673
Date: 2021-04
Rights: Attribution-NonCommercial-NoDerivatives 4.0 International
Related Publications: 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


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