Phys. Rev. A 71, 022322 (2005) [6 pages]

Suboptimal quantum-error-correcting procedure based on semidefinite programming

Abstract

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Naoki Yamamoto^*, Shinji Hara^†, and Koji Tsumura^‡
Department of Information Physics and Computing, Graduate School of Information Science and Technology, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

Received 28 July 2004; published 28 February 2005

In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the one-to-one parametrization of quantum channels, a procedure finding a suboptimal error-correcting channel based on a semidefinite programming is proposed. The effectiveness of our method is verified by an example of the bit-flip channel decoding.

URL:

http://link.aps.org/doi/10.1103/PhysRevA.71.022322

DOI:

10.1103/PhysRevA.71.022322

PACS:

03.67.Pp, 02.60.Pn

^*Also at Control and Dynamical Systems, California Institute of Technology, Pasadena, California 91125. Electronic address: naoki@cds.caltech.edu

^†Electronic address: Shinji_Hara@ipc.i.u-tokyo.ac.jp

^‡Electronic address: Koji_Tsumura@ipc.i.u-tokyo.ac.jp

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Phys. Rev. A 71, 022322 (2005) [6 pages]

Suboptimal quantum-error-correcting procedure based on semidefinite programming