2006/08/31 by David W. Kribs, Robert W. Spekkens · 53 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic operation #Algorithm #Artificial intelligence #Computer science #Control theory (sociology) #Dual (grammatical number) #Identification (biology) #Mathematical analysis #Mathematics #Noise (video) #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum error correction #Quantum mechanics #Theoretical computer science #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.74.042329
published in Physical Review A 74(4) (American Physical Society) · Physical Review A, to appear, 8 pages
arxiv created 2006/09/29 · openalex publication_date 2006/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from subsequent iterations of the noise. We also demonstrate that in the case of unital noise operations one can identify a subset of all correctable subsystems---those that can be corrected by a single unitary operation---as the noiseless subsystems for the composition of the noise operation with its dual. Using the recently developed structure theory for noiseless subsystems, the identification of such unitarily correctable subsystems is reduced to an algebraic exercise.