High performance entanglement-assisted quantum LDPC codes need little entanglement

Understand

Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use.

• It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states.
• We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length.
• Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is.