Title: Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels,
Abstract: Quantum entanglement serves as a valuable resource for many important quantum
operations. A pair of entangled qubits can be shared between two agents by
first preparing a maximally entangled qubit pair at one agent, and then sending
one of the qubits to the other agent through a quantum channel. In this
process, the deterioration of entanglement is inevitable since the noise
inherent in the channel contaminates the qubit. To address this challenge,
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. This paper put forth two
recurrence QED algorithms that adapt to the quantum channel to tackle the
efficiency issue. The proposed algorithms have guaranteed convergence for
quantum channels with two Kraus operators, which include phase-damping and
amplitude-damping channels. Analytical results show that the convergence speed
of these algorithms is improved from linear to quadratic and one of the
algorithms achieves the optimal speed. Numerical results confirm that the
proposed algorithms significantly improve the efficiency of QED.