# Efficient Entanglement Distillation for Quantum Channels with Polarization Mode Dispersion

## TL;DR

This paper introduces an efficient recurrence quantum entanglement distillation algorithm tailored for photonic qubits affected by polarization mode dispersion in optical fibers, significantly improving convergence speed and success probability.

## Contribution

The paper presents a novel recurrence QED algorithm that achieves optimal fidelity and success probability, with quadratic convergence, for entanglement distribution over PMD-affected fiber channels.

## Key findings

- Achieves optimal fidelity in each distillation round.
- Converges quadratically, reducing the number of rounds needed.
- Provides an efficient method for high-fidelity entanglement distribution.

## Abstract

Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing entanglement with high-quality via fiber optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences in the system. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements on both the size of the quantum circuits involved and on the initial quality of entanglement in particles. However, because the number of particles required grows exponentially with the number of rounds of distillation, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditional on the optimal fidelity being achieved) in every round of distillation. The attainment of optimal fidelity improves the convergence speed of fidelity with respect to the rounds of distillation from linear to quadratic, and hence significantly reduces the number of distillation rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with high fidelity via optic fibers.