Practical Entanglement Distillation Scheme Using Recurrence Method And Quantum Low Density Parity Check Codes

TL;DR

This paper explores an improved entanglement distillation scheme that replaces traditional hashing with efficiently decodable quantum codes, notably QLDPC codes, achieving higher yields in practical scenarios.

Contribution

It introduces a practical entanglement distillation method using recurrence and QLDPC codes, demonstrating significant yield improvements over existing approaches.

Findings

QLDPC codes outperform other codes in yield

Yield exceeds 25% compared to the next best method

Effective for Werner states across various noise levels

Abstract

Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice. In this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code is found to give the highest yield for Werner states over a wide range of noise level --- the yield for using this QLDPC code is higher than the first runner up by more than 25\% over a wide parameter range. In this respect, the effectiveness of using QLDPC codes in practical entanglement distillation is illustrated.