Division of Physics, Mathematics, and Astronomy, California Institute of Technology, MC 253-37, Pasadena, California 91125, USA.
Phys Rev Lett. 2013 Apr 26;110(17):170501. doi: 10.1103/PhysRevLett.110.170501. Epub 2013 Apr 22.
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which quantum errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable.
已知的量子错误纠正方案通常只能利用有限的一类经典纠错码。纠缠辅助量子纠错是一种部分解决方案，它使得在二进制或四进制有限域上利用任何经典线性码成为可能。然而，已知的纠缠辅助方案需要无噪声的量子位来帮助纠正噪声量子位上的量子错误，这可能是一个过于苛刻的假设。我们通过提出编码和解码操作来证明，通过辅助量子位来辅助，这些量子位可能会出现一种特定类型的量子错误，这种假设更加宽松和现实。与纠缠辅助一样，我们的方案可以导入任何二进制或四进制线性码。如果辅助量子位是无噪声的，那么当底层经典码是最大距离可分离时，我们的码就成为纠缠辅助码，并饱和量子Singleton 界。
