Exact solution for the max-min quantum error recovery problem

Naoki Yamamoto

doi:10.1109/CDC.2009.5400142

Exact solution for the max-min quantum error recovery problem

Naoki Yamamoto

Department of Applied Physics and Physico-Informatics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational tools. Nevertheless, it is shown that, when the input takes a qubit, the problem is exactly convex for any size of error process. The Sum of Squares (SOS) characterization of a specific class of polynomial functions plays a crucial role in deriving this result.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1433-1438
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400142
Publication status	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 2009 Dec 15 → 2009 Dec 18

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	09/12/15 → 09/12/18

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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10.1109/CDC.2009.5400142

Cite this

Yamamoto, N. (2009). Exact solution for the max-min quantum error recovery problem. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 1433-1438). Article 5400142 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400142

Exact solution for the max-min quantum error recovery problem. / Yamamoto, Naoki.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 1433-1438 5400142 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yamamoto, N 2009, Exact solution for the max-min quantum error recovery problem. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400142, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1433-1438, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 09/12/15. https://doi.org/10.1109/CDC.2009.5400142

Yamamoto N. Exact solution for the max-min quantum error recovery problem. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 1433-1438. 5400142. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400142

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Exact solution for the max-min quantum error recovery problem

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