Good quantum error-correcting codes exist
- 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, Vol. 54, Issue 2; Other Information: PBD: Aug 1996
- Country of Publication:
- United States
- Language:
- English
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