Approximate quantum error correction, random codes, and quantum channel capacity

Journal Article · Fri Jun 15 00:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.062315· OSTI ID:20991100

Klesse, Rochus ^[1]

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1. Universitaet zu Koeln, Institut fuer Theoretische Physik, Zuelpicher Strasse 77, D-50937 Cologne (Germany)

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This result is then used to analyze the average error correcting performance of codes that are randomly drawn from unitarily invariant code ensembles. Our results confirm that random codes of sufficiently large block size are highly suitable for quantum error correction. Moreover, employing a lemma of Bennett, Shor, Smolin, and Thapliyal, we prove that random coding attains information rates of the regularized coherent information.

• OSTI ID: 20991100
• Journal Information: Physical Review. A, Vol. 75, Issue 6; Other Information: DOI: 10.1103/PhysRevA.75.062315; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CAPACITY
CORRECTIONS
INFORMATION THEORY
NOISE
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
RANDOMNESS