A characterization of entanglement-assisted quantum low-density parity-check codes
arXiv:1108.0679 · doi:10.1109/TIT.2013.2247461
Abstract
As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) 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.
7 pages, no figures, final accepted version for publication in the IEEE Transactions on Information Theory
References in corpus (7)
- Correcting Quantum Errors with Entanglement
- Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding
- General entanglement-assisted quantum error-correcting codes
- Entanglement-assisted quantum low-density parity-check codes
- Quantum Error Correction beyond the Bounded Distance Decoding Limit
- On the logical operators of quantum codes
- A combinatorial approach to X-tolerant compaction circuits
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- Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1