  Quantum entanglement distillation is a process to extract a small number of
high-fidelity entanglement from a large number of low-fidelity ones, which in
essence is to trade yield (or survival rate) for fidelity. Among existing
distillation approaches, Gisin's local filtering protocol is commonly adopted
in photonic quantum systems for distilling entangled photons in polarization
basis. Yet, the performance of Gisin's filter is cursed by the same fundamental
trade-off between fidelity and yield. To address this challenge, in this work,
we propose a protocol to recycle the disposed photons and improve their
fidelity by a designed (and optimized) local operator. The key parameters of
the proposed protocol are calculated by solving a constrained optimization
problem. In so doing, we achieve significantly higher yield of high-fidelity
entanglement pairs. We further evaluate the performance of our designed
protocol under two common configurations of Gisin's filter, namely full filter
and partial filter. Compared with existing distillation protocols, the results
demonstrate that our design achieves as much as 31.2% gain in yield under the
same fidelity, while only incurring moderate system complexity in terms of
invested hardware and extra signaling for synchronization.
