A characterization of entanglement-assisted quantum low-density parity-check codes

TL;DR

This paper characterizes quantum LDPC codes that use only one ebit by establishing necessary and sufficient conditions, expanding the understanding of their structure and potential for practical quantum error correction.

Contribution

It provides a complete characterization of entanglement-assisted quantum LDPC codes that require only one ebit, including conditions for their existence and their parameter spectrum.

Findings

Identifies conditions for quantum LDPC codes with a single ebit

Analyzes the range of achievable code parameters

Advances understanding of quantum code structures

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.