Good quantum error-correcting codes exist

A. R. Calderbank, Peter W. Shor · 1996 · Phys. Rev. A 54, 1098

| 编号 QE005 | 主题 基础理论 | 链接 arXiv:quant-ph/9512032 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate $k/n=1-2H_2(2t/n)$ where $H_2(p)$ is the binary entropy function $-p{\log }_{2}p-(1-p){\log }_2(1-p)$ . Upper bounds on this asymptotic rate are given. PACS numbers: 03.65.Bz

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