  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.
