Practical entanglement distillation scheme using recurrence method and quantum low density parity check codes

Many entanglement distillation schemes use either universal random hashing or breading as their final step to obtain shared almost perfect EPR pairs. Both methods involve random stabilizer quantum error-correcting codes whose syndromes can be measured using simple and efficient quantum circuits. When applied to high fidelity Werner states, the highest yield protocol among those using local Bell measurements and local unitary operations is the one that uses a certain breading method. And random hashing method losses to breading just by a thin margin. In spite of their high yield, the hardness of decoding random linear code makes the use of random hashing and breading infeasible in practice. In this pilot study, we analyze the performance of recurrence method, a well-known entanglement distillation scheme, by replacing the final random hashing or breading procedure by various efficiently decodable quantum codes. We find that among all the replacements we have investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code gives the highest yield for Werner states of almost all noise level. In this respect, our finding illustrates the effectiveness of using QLDPC codes in practical entanglement distillation.