Quantum Lost and Found
arXiv:quant-ph/0209025 · doi:10.1080/09500340308234541
Abstract
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give a conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme (2) for some basis B there is a correcting measurement M (3) for all bases B there is an M (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.
14 pages, 1 eps-Fig, revtex4+amsfonts
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