Entanglement-Assisted Quantum Turbo Codes
Entanglement-Assisted Quantum Turbo Codes
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DOI：
10.1109/tit.2013.2292052
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发表时间：
2014-02-01
影响因子：
2.5
通讯作者：
Babar, Zunaira
中科院分区：
文献类型：
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作者：
Wilde, Mark M.;Hsieh, Min-Hsiu;Babar, Zunaira
现有量子串行涡轮编码理论的一个意想不到的故障是量子卷积编码器不能同时是递归的和非灾难性的。这些性质分别是量子Turbo码族具有最小距离随块长增长和迭代译码算法收敛所必需的。在这里，我们表明，纠缠辅助范式简化了量子Turbo码的理论，在这个意义上，纠缠辅助量子（EAQ）卷积编码器可以拥有上述两个理想的属性。我们给出了几个递归和非灾难性的EAQ卷积编码器的例子，并详细说明了它们的相关参数。然后，我们修改Poulin等人的量子Turbo解码算法，为了使组成解码器彼此之间仅传递沿着外部信息而不是如Poulin等人的解码器中那样传递后验概率，并且这导致无辅助量子turbo码的性能的显著改进。其他模拟结果表明，纠缠辅助Turbo码可以可靠地工作在一个噪声制度4.73分贝超出标准的量子Turbo码，当使用在一个无记忆的去极化信道。此外，我们的几个量子Turbo码是在1 dB或更少的散列限制，使量子Turbo码的性能，现在是与经典的Turbo码。最后，我们证明了纠缠是使卷积编码器成为非灾难性和递归的资源，因为仅作用于信息量子位、经典位、规范量子位和辅助量子位的编码器不能同时满足它们。
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with block-length and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin et al., in order to have the constituent decoders pass along only extrinsic information to each other rather than a posteriori probabilities as in the decoder of Poulin et al., and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.