Analysis of Efficient Recurrence Quantum Entanglement Distillation

Quantum entanglement serves as a valuable resource for many important quantum operations. To address challenge brought by the noise in the quantum channel, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. To enable efficient QED algorithms, it is essential to increase the fidelity of the qubit pairs obtained in each rounds of distillation, so as to reduce the rounds of distillation required. This paper considers two-Kraus-operator (TKO) channels, a class that covers several typical quantum channels, characterizes the optimal fidelity achievable by QED operations in each round, and designs recurrence algorithms which achieve the optimal fidelity.