Entanglement-Assisted Quantum Turbo Codes

• Published in: IEEE transactions on information theory Vol. 60; no. 2; pp. 1203 - 1222
• Main Authors: Wilde, Mark M., Min-Hsiu Hsieh, Babar, Zunaira
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Classical and quantum physics: mechanics and fields; Coders; Codes; Coding theory; Coding, codes; Complexity theory; Convolutional codes; Decoders; Decoding; Encoders; entanglement-assisted quantum error correction; entanglementassisted quantum convolutional code; entanglementassisted quantum turbo code; Exact sciences and technology; Information theory; Information, signal and communications theory; Miscellaneous; Noise levels; non-catastrophic; Physics; Quantum communication; Quantum entanglement; Quantum information; Quantum theory; Qubits (quantum computing); Recursive; Signal and communications theory; Simulation; Telecommunications and information theory; Turbo codes; Performance evaluation; Convolutional code; Coding circuit; Turbo code; Algorithm; Iterative decoding; recursive; entanglement-assisted quantum turbo code; Memoryless channel; entanglement-assisted quantum error correction; non-catastrophic; Posterior probability; Simulation; Hashing; Recursive method; entanglement-assisted quantum convolutional code; Minimal distance; Quantum information; Error correction; Quantum communication; Damaging
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2292052

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. We then modify the quantum turbo decoding algorithm of Poulin , 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 , 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.