Superiority of 2-EPPs to 1-EPPs with finite entangled resources

If the number of initial entanglement pairs shared between two parties (Alice and Bob) is infinite, it is known that one-way entanglement purification protocols (1-EPPs) can perform as well as two-way entanglement purification protocols (2-EPPs) in a noisy quantum channel, whose characteristics are equal to those of a classical channel. However, when EPPs are applied in actual quantum information systems, the number of shared initial entanglement pairs is necessarily finite. In this paper, we consider the application of 1-EPPs and 2-EPPs to finite entanglement pairs that are initially shared between two parties over a phase damping channel. In this case, we demonstrate that 2-EPPs outperform 1-EPPs.