# Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

## TL;DR

This paper introduces adaptive recurrence quantum entanglement distillation algorithms tailored for two-Kraus-operator channels, significantly enhancing efficiency and convergence speed in entanglement purification processes.

## Contribution

The paper proposes two new adaptive recurrence QED algorithms with guaranteed quadratic convergence for channels with two Kraus operators, improving upon existing methods.

## Key findings

- Algorithms achieve quadratic convergence speed.
- Numerical results show significant efficiency improvements.
- Algorithms are effective for phase-damping and amplitude-damping 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.