Heralded entanglement concentration for photon systems with linear-optical elements

Abstract

We present two nonlocal entanglement concentration protocols (ECPs) to distill a subset of N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state or a W state from a set of photon systems in a partially entangled GHZ-like pure state or a less-entangled W-like state with known parameter, respectively. Our ECPs have some advantages. First, our ECPs work in a heralded way with linear-optical elements only, without the postselection based on nonlinear optics, far different from the previous ECPs. Second, they require only a copy of the less-entangled photon system in each round of the entanglement concentration process, not two copies, which decreases the difficulty of their implementation in experiment largely. Third, our ECPs avoid checking the photon number in the output modes of linear-optical elements with the sophisticated single-photon detectors. Moreover, all parties can operate the process for concentration simultaneously and independently, which leads to flexible operations and improves the performance greatly in experiment. These advantages make our ECPs useful in practical applications in long-distance quantum communication network.