Collective decoherence is possible if the departure between quantum bits is smaller than the effective wave length of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two qubits are enough to protect one bit quantum information, and approximately $L+ 1/2 \log_2((\pi L)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large. For preventing collective amplitude damping, these codes are much more efficient than the previously-discovered quantum error correcting or avoiding codes.
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机译：如果量子位之间的距离小于噪声场的有效波长，则可能会发生集体退相干。退相干的集体性有助于我们设计出更有效的量子代码。我们提出了一类最佳的量子代码，以防止在零温度下对储层的集体振幅阻尼。结果表明，两个量子位足以保护一位量子信息，当$ L $大时，大约$ L + 1/2 \ log_2（（\ pi L）/ 2）$量子位足以保护$ L $量子位信息。 。为了防止集体振幅阻尼，这些代码比以前发现的量子误差校正或避免代码要有效得多。
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