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Journal of the Optical Society of America B

Linear-optics-based entanglement concentration of unknown partially entangled three-photon W states

Hong‐Fu Wang, Shou Zhang, Kyu-Hwang Yeon

Published Sep 29, 2010• 47 citations
Publisher

Abstract

We propose two experimental schemes for concentrating entanglement in unknown partially entangled three-photon W states with only linear optical elements and the conventional photon detectors. We first propose a heralded scheme using a heralded controlled-NOT (CNOT) gate between two photons. Then we simplify this method to a post-selected one requiring time entanglement of the input photons without using ancillary photons. In the two schemes, Alice, Bob, and Charlie at three distant parties can obtain one maximally entangled three-photon W state from two identical partially entangled three-photon W states, taking the specific form of α|H>|H>|V>+β(|H>|V>|H>+|V>|H>|H>), by local operations and classical communication. We discuss and consider the success probabilities and the practical realizations of the schemes.

DOI
10.1364/josab.27.002159

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We present two three-photon entanglement concentration protocols (ECPs) for an arbitrary unknown less-entangled W-class state, resorting to linear optical elements. In our normal ECP, the three parties can obtain a three-photon system in a standard W state probabilistically, similar to the Schmidt projection method. In our improved ECP, the parties obtain not only some higher-fidelity partially entangled three-photon systems but also some entangled two-photon systems in each round of concentration with two copies of three-photon systems. It is interesting to show that the three-photon and two-photon systems kept after a round of concentration have the same parameters. The parties can obtain some three-photon systems in a standard W state with a far higher success probability than the normal ECP, by exploiting the three-photon and two-photon systems with the same parameters as the resource for the next round of concentration. Both of these ECPs may have good applications in quantum communication in the future.
We propose a single-photon-assisted entanglement concentration protocol (ECP) for nonlocal N-photon systems in a partially entangled pure W-class state with linear optical elements. Only one of the N parties in quantum communication prepares an ancillary photon and operates the entanglement concentration process for picking up the standard N-photon W state from each partially entangled pure W-class state by choosing the two-mode instances from a polarization beam splitter. Compared with other ECPs for W-class states, our protocol has some advantages. First, it requires only linear optical elements. Second, it requires an N-photon system and an ancillary photon for each round of concentration, not two systems. Third, only one party asks other parties to retain or discard their photons. All these advantages make our ECP more feasible and more convenient than others.