Exact solution for the max-min quantum error recovery problem

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 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 languageEnglish
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages1433-1438
Number of pages6
DOIs
Publication statusPublished - 2009 Dec 1
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: 2009 Dec 152009 Dec 18

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period09/12/1509/12/18

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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  • 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). [5400142] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400142