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Journal of the Optical Society of America B

Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity

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

Published Mar 16, 2012• 33 citations
Publisher

Abstract

We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B28, 2030 (2011)]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.

DOI
10.1364/josab.29.000630

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We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B28, 2030 (2011)]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.
We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In these schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W states with a certain success probability. Finally, we discuss the influence of sources of error and decoherence on the schemes. The proposed setup only employs some linear optical elements and the cross-Kerr medium, which greatly reduces the difficulty of experimental realization. These schemes are feasible with current experimental technology.
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.
We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state. As a pioneering three-step entanglement concentration scheme, our protocol only needs a single-photon resource to assist the concentration in each step, which makes this protocol more economical. With the help of the linear optical elements and weak cross-Kerr nonlinearity, one can obtain a maximally-entangled cluster state via local operations and classical communication. Moreover, the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.
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.
We propose a nonlocal entanglement concentration protocol (ECP) for N-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state, and it is the resource in the next round of entanglement concentration. By iterating the entanglement concentration process several times, the present ECP has a total success probability approaching the limit in theory. The present ECP has the advantage of a high success probability. Moreover, the present ECP requires only the N-photon system itself and some ancillary single photons, not two copies of the systems, which decreases the difficulty of its implementation greatly in experiment. It may have good applications in quantum communication in the future.
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states---i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this protocol feasible with present techniques. By iteration of entanglement concentration processes, this scheme has a higher efficiency and yield than those with linear optical elements. All these advantages make this scheme more efficient and more convenient than others in practical applications.