Enhancing Entanglement Purification with Shared Randomness

Entanglement purification protocols are essential for improving entanglement distribution fidelity in quantum networks. We show that shared randomness, a free classical resource, can improve entanglement purification performance with a simple but effective strategy. We analyze a representative scenario where two entanglement sources independently distribute Bell-diagonal states to two remote parties with buffer quantum memories, who can apply the standard 2-to-1 DEJMPS protocol, but do not know which source each distributed entangled state comes from within an entanglement distribution round. When the two parties exploit shared randomness to accumulate and randomly shuffle the 2N entangled states coming from N entanglement distribution rounds before purification, the effective input state becomes more symmetric, leading to a provable improvement in both success probability and any entanglement quality metric that monotonically increases with Bell fidelity. This enhancement holds for arbitrary non-identical entanglement sources with moderate and equal bias for the undetectable error, and remains robust under realistic quantum memory decoherence when storing the earlier-distributed entangled states, provided that the two sources are not nearly identical. Our results establish that classical shared randomness can genuinely improve quantum communication performance without modifying the underlying physical operations.