Physics – Quantum Physics
Scientific paper
2010-06-07
Phys. Rev. A 82 062306 (2010)
Physics
Quantum Physics
29 pages, 19 examples. Contains complete proofs for all the theorems in arXiv:0705.4282
Scientific paper
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., "noiseless", "unitarily correctible", etc.) and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational critera, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.
Blume-Kohout Robin
Ng Hui Khoon
Poulin David
Viola Lorenza
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