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Chinese Physics

Scheme for entanglement concentration of unknown W class states via linear optics

Zhang Li-hua, Dong Ping, Zhuo‐Liang Cao

Published Feb 26, 2007• 4 citations
Publisher

Abstract

This paper proposes a scheme for entanglement concentration of unknown triparticle W class states with a certain probability. This protocol is mainly based on the coincidences of single-photon detectors and requires single-photon detectors and linear optical elements. The scheme is feasible within current technology.
DOI
10.1088/1009-1963/16/3/014

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The entanglement concentration protocols (ECPs) are presented for distilling the maximally entangled state from a known partially entangled n-photon Bell-class and W state, respectively, only resorting to the linear optical elements and quantum nondemolition detector. Different from the traditional parity check with a single photon as an ancilla, we use linear optical elements for changing the photon paths to realize the concentration. The total success probability of the concentration for n-photon entangled states is calculated. The present protocols only require a partially entangled state and do not need any single auxiliary particle. By iterating the ECP repeatedly, the maximal success probability can be increased. Meanwhile, the present protocols are more suitable for the photon system due to the simple operations.
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.
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 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.