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Journal of Physics B Atomic Molecular and Optical Physics

Near-deterministic generation of four-modeW-type entangled coherent states

Yu Guo, Le‐Man Kuang

Published Aug 7, 2007• 25 citations
Publisher

Abstract

In this paper, we propose an optical scheme to generate four-mode W -type entangled coherent states (ECSs) in free travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. Our scheme consists of a symmetric optical setup in which there are two Mach–Zehnder interferometers in which each arm contains a cross-Kerr medium. We calculate the average fidelity of generated W -type ECSs, the success probability of producing four-mode W -type ECSs and the average fidelity of the generated four-mode W -type ECSs. It is indicated that our protocol is nearly deterministic.

DOI
10.1088/0953-4075/40/16/011

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In this paper, we propose an optical scheme to generate four-mode W -type entangled coherent states (ECSs) in free travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. Our scheme consists of a symmetric optical setup in which there are two Mach–Zehnder interferometers in which each arm contains a cross-Kerr medium. We calculate the average fidelity of generated W -type ECSs, the success probability of producing four-mode W -type ECSs and the average fidelity of the generated four-mode W -type ECSs. It is indicated that our protocol is nearly deterministic.
In this paper, we propose an optical scheme to generate three-mode W -type entangled coherent states (ECSs) in free-travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. The success probability of our protocol approaches unity in the ideal case. We also analyse that our scheme can be generalized to produce other N -mode W -type ECSs ( N ≠ 2 n ) nearly deterministically through choosing the beam splitters with appropriate reflectance.
We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.
Trio coherent states (TCSs) are non-Gaussian three-mode entangled states which can serve as a useful resource for continuous-variable quantum tasks, so their generation is of primary importance. Schemes exist to generate stable TCSs in terms of vibrational motion of a trapped ion inside a crystal. However, to perform quantum communication and distributed quantum computation the states should be shared beforehand among distant parties. That is, their modes should be able to be directed to different desired locations in space. In this work, we propose an experimental setup to generate such free-traveling TCSs in terms of optical fields. Our scheme uses standard physical resources, such as coherent states, balanced beam splitters, phase shifters, nonideal on-off photodetectors, and realistic weak cross-Kerr nonlinearities, without the need of single photons or homodyne or heterodyne measurements. We study the dependences of the fidelity of the state generated by our scheme with respect to the target TCS and the corresponding generation probability for the parameters involved. In theory, the fidelity could be nearly perfect for whatever weak nonlinearities $\ensuremath{\tau}$ and low photodetector efficiency $\ensuremath{\eta}$, provided that the amplitude $|\ensuremath{\alpha}|$ of an input coherent state is large enough, namely, $|\ensuremath{\alpha}|\ensuremath{\ge}5/(\sqrt{\ensuremath{\eta}}\ensuremath{\tau})$.