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arXiv:quant-ph/0606109 · Physical Review A

Greenberger-Horne-Zeilinger–type and W -type entangled coherent states: Generation and Bell-type inequality tests without photon counting

Hyunseok Jeong, Nguyen Ba An

Published Aug 17, 2006• 118 citations
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Abstract

We study Greenberger-Horne-Zeilinger--type (GHZ-type) and $W$-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for $W$-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate $W$-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the $W$-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

DOI
10.1103/physreva.74.022104

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An optical realization of the Greenberger, Horne, Zeilinger (GHZ) state is proposed for testing local realistic theories. The optical GHZ states in this case are three-mode entangled coherent states and the relevant observable used to perform tests of quantum mechanics against local realistic theories is photon number parity. The amplitudes of the coherent states need to be mesoscopic if significant losses are involved but may be macroscopic if losses are minimal. A method is proposed for generating the required GHZ state that amounts to an extension of a proposal previously discussed (C.C. Gerry, Phys. Rev. A 59 4095 (1999)) for generating macroscopic superposition states of travelling wave fields.
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In this paper we propose a scheme for creating a three photons Greenberger-Horne-Zeilinger-type (GHZ) state using only linear optics elements and single-photon detectors. We furthermore generalize the scheme for producing any GHZ-like state of n photons. The input state of the scheme consists of a nonentangled state of n photons. Experimental aspects regarding the implementation of the scheme are presented. Finally, the role of such schemes in quantum information processing with photons is discussed.