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Journal of Physics B Atomic Molecular and Optical Physics

Perfect entanglement concentration of an arbitrary four-photon polarization entangled state via quantum nondemolition detectors

Meiyu Wang, Fengli Yan, Jingzhou Xu

Published Jul 5, 2016• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/49/15/155502

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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.
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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 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.
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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.