Information-preserving structures: A general framework for quantum zero-error information
Abstract
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 natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational criteria, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.
Additional Information
© 2010 The American Physical Society. Received 27 August 2010; published 7 December 2010. The authors acknowledge support in part by the Gordon and Betty Moore Foundation (D.P. and H-K.N.); by the Natural Sciences and Engineering Research Council of Canada and Fonds Québécois de la Recherche sur la Nature et les Technologies (D.P.); by the National Science Foundation under Grants No. PHY-0803371, No. PHY-0456720, No.PHY-0555417, and No. PHY-0903727 (L.V.); and by the Government of Canada through Industry Canada and the Province of Ontario through the Ministry of Research & Innovation (R.B.K.). We also gratefully acknowledge extensive conversations with Robert Spekkens, Daniel Gottesman, Cedric Beny, and Wojciech Zurek.Attached Files
Published - BlumeKohout2010p12952Phys_Rev_A.pdf
Files
Name | Size | Download all |
---|---|---|
md5:cf2844f4b474207549dba753a609f789
|
692.4 kB | Preview Download |
Additional details
- Eprint ID
- 22882
- Resolver ID
- CaltechAUTHORS:20110315-091122301
- Gordon and Betty Moore Foundation
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Fonds Québécois de la Recherche sur la Nature et les Technologies
- PHY-0803371
- NSF
- PHY-0456720
- NSF
- PHY-0555417
- NSF
- PHY-0903727
- NSF
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research & Innovation
- Created
-
2011-03-15Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field