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Chinese Physics B

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

Bin Si, Shi‐Lei Su, Li-Li Sun, Liu‐Yong Cheng, Hong‐Fu Wang, Shou Zhang

Published Mar 1, 2013• 23 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/22/3/030305

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We present a protocol for concentrating an arbitrary four-photon entangled state into a maximally entangled state assisted with singled photons. The concentration protocol uses the linear optics and the cross-Kerr nonlinearity based on the post selection principle. Four parties called Alice, Bob, Charlie and Dan in different distant locations can obtain the cluster state from an arbitrary entangled four-photon state with a certain probability. Quantum non-demolition (QND) measurements are available in this protocol. Moreover, this scheme can be steady with a higher success possibility.
We present two two-step practical entanglement concentration protocols for concentrating an arbitrary three-particle less-entangled WWW state into a maximally entangled WWW state assisted with single photons. The first protocol uses the linear optics and the second protocol adopts the cross--Kerr nonlinearity to perform the protocol. In the first protocol, based on the postselection principle, three parties say Alice, Bob, and Charlie in different distant locations can obtain the maximally entangled WWW state from the arbitrary less-entangled WWW state with a certain success probability. In the second protocol, the parties are not required to possess the sophisticated single-photon detectors and the concentrated photon pair can be retained after performing this protocol successfully. Moreover, the second protocol can be repeated to get a higher success probability. Both protocols may be useful in practical quantum-information applications.
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.
Cluster states, whose model are a remarkably rich structure in measurement-based quantum computation, hold high degree of entanglement, while entanglement is very fragile during the process of transmission because of the inevitable interaction with the environment. We propose two entanglement concentration protocols for four-particle linear cluster states which and are susceptible to the decoherence and the imperfect communication setups. In the first protocol, POVM operators are introduced to maximize the success probability, and the second protocol is based on cross-Kerr nonlinearity which is utilized to check the parity between the original particle and the ancillary particle. Both of the protocols have their own advantages. The first one can be easily realized in experiment by linear optics, while the one with cross-Kerr nonlinearity reach more than 90% success probability by iteration. Since the wide application of cluster states, the two protocols are efficient and valuable to different fields of quantum communication.
Abstract We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.