Good quantum error-correcting codes exist

Journal Article · Thu Aug 01 04:00:00 EDT 1996 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.54.1098· OSTI ID:286597

Calderbank, A R; Shor, P W ^[1]

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1. AT&T Research, 600 Mountain Avenue, Murray Hill, New Jersey 07974 (United States)

A quantum error-correcting code is defined to be a unitary mapping (encoding) of {ital k} qubits (two-state quantum systems) into a subspace of the quantum state space of {ital n} qubits such that if any {ital t} of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting {ital n} qubits can be used to faithfully reconstruct the original quantum state of the {ital k} encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate {ital k}/{ital n}=1{minus}2{ital H}{sub 2}(2{ital t}/{ital n}) where {ital H}{sub 2}({ital p}) is the binary entropy function {minus}{ital p}log{sub 2}{ital p}{minus}(1{minus}{ital p})log{sub 2}(1{minus}{ital p}). Upper bounds on this asymptotic rate are given. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 286597
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 54; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
COHERENT STATES
COMPUTER CODES
COMPUTERS
ENTROPY
ERRORS
INFORMATION THEORY
QUANTUM MECHANICS