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

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.