Mark M. Wilde, Min-Hsiu Hsieh
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 blocklength 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. Simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 5.5 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Entanglement is the resource that enables a convolutional encoder to satisfy both properties because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.
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http://arxiv.org/abs/1010.1256
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