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A Characterization of Entanglement-Assisted Quantum Low-Density Parity-Check Codes

Fujiwara, Yuichiro and Tonchev, Vladimir D. (2013) A Characterization of Entanglement-Assisted Quantum Low-Density Parity-Check Codes. IEEE Transactions on Information Theory, 59 (6). pp. 3347-3353. ISSN 0018-9448. doi:10.1109/TIT.2013.2247461.

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As in classical coding theory, quantum analogs of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane construction. However, special requirements in the quantum setting severely limit the structures such quantum codes can have. While the entanglement-assisted stabilizer formalism overcomes this limitation by exploiting maximally entangled states (ebits), excessive reliance on ebits is a substantial obstacle to implementation. This paper gives necessary and sufficient conditions for the existence of quantum LDPC codes which are obtainable from pairs of identical LDPC codes and consume only one ebit, and studies the spectrum of attainable code parameters.

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Additional Information:© 2013 IEEE. IEEE Open Access. Manuscript received August 02, 2011; revised June 12, 2012; accepted October 05, 2012. Date of publication February 14, 2013; date of current version May 15, 2013. This work was supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research 20.5897 and JSPS Postdoctoral Fellowships for Research Abroad (YF) and in part by the NSA Grants H98230-10-1-0177 and H98230-12-0213 (VDT). This paper was presented in part at the Second International Conference on Quantum Error Correction, Los Angeles, CA, December 2011. The authors would like to thank Mark M. Wilde, the anonymous referee and Associate Editor Jean-Pierre Tillich for their insightful comments and valuable suggestions. This research was conducted when the first author was visiting the Department of Mathematical Sciences, Michigan Technological University. He thanks the department for its hospitality.
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)20.5897
National Security Agency (NSA)H98230-10-1-0177
National Security Agency (NSA)H98230-12-0213
Subject Keywords:Entanglement-assisted quantum error correction, low-density parity-check (LDPC) code, pairwise balanced design, stabilizer code, Steiner 2-design
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INSPEC Accession Number13499518
Issue or Number:6
Record Number:CaltechAUTHORS:20130805-091648852
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Official Citation:Fujiwara, Y.; Tonchev, V.D., "A Characterization of Entanglement-Assisted Quantum Low-Density Parity-Check Codes," Information Theory, IEEE Transactions on , vol.59, no.6, pp.3347,3353, June 2013 doi: 10.1109/TIT.2013.2247461
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39753
Deposited By: Tony Diaz
Deposited On:05 Aug 2013 23:22
Last Modified:09 Nov 2021 23:46

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