Abstract
A quantum error-correcting code is defined to be a unitary mapping (encoding)\nof k qubits (2-state quantum systems) into a subspace of the quantum state\nspace of n qubits such that if any t of the qubits undergo arbitrary\ndecoherence, not necessarily independently, the resulting n qubits can be used\nto faithfully reconstruct the original quantum state of the k encoded qubits.\nQuantum error-correcting codes are shown to exist with asymptotic rate k/n = 1\n- 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log\n(1-p). Upper bounds on this asymptotic rate are given.\n
Keywords
Quantum error correctionQubitMathematicsQuantum mechanicsDiscrete mathematicsQuantumPhysics
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Publication Info
- Year
- 1996
- Type
- article
- Volume
- 54
- Issue
- 2
- Pages
- 1098-1105
- Citations
- 2414
- Access
- Closed
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Cite This
A.R. Calderbank,
Peter W. Shor
(1996).
Good quantum error-correcting codes exist.
Physical Review A
, 54
(2)
, 1098-1105.
https://doi.org/10.1103/physreva.54.1098
Identifiers
- DOI
- 10.1103/physreva.54.1098
- PMID
- 9913578
- arXiv
- quant-ph/9512032