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Modern Physics Letters B

CONCENTRATING ARBITRARY FOUR-PHOTON LESS-ENTANGLED CLUSTER STATE BY SINGLE PHOTONS

Ting-Ting Xu, Wei Xiong, Liu Ye

Published Nov 15, 2012• 14 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984912502144

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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.
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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.
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.
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.
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 put forward two efficient entanglement concentration protocols (ECPs) for distilling the maximally entangled NOON state from arbitrary less-entangled NOON state with only an auxiliary single photon. With the help of the weak cross-Kerr nonlinearities, both the two ECPs can be used repeatedly to get a high success probability. In the first ECP, the auxiliary single photon should be shared by the two parties say Alice and Bob. In the second ECP, the auxiliary single photon is only possessed by Bob, which can greatly increase the practical success probability by avoiding the transmission loss. Moreover, Bob can operate the whole protocol alone, which makes the protocol more simple. Therefore, our two ECPs, especially the second ECP may be more useful and convenient in the current quantum information processing.