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Acta Physica Sinica

Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities

Ding Dong, Yan Feng-Li

Published Jan 1, 2013• 5 citations
Publisher

Abstract

The scheme for quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger (GHZ)-state is proposed based on weak nonlinearities and linear-optics elements. We first describe a scheme of the symmetry analyzer for two-photon Bell-state by using beam splitters and cross-Kerr nonlinear medium. According to this symmetry analyzer for two-photon Bell-state and the controlled-NOT gates we construct a three-photon state analyzer which can completely and nondestructively discriminate eight three-photon GHZ states.

DOI
10.7498/aps.62.100304

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We present a simple method for the complete analysis of the maximally hyperentangled state in polarization and spatial-mode degrees of freedom assisted by the weak cross-Kerr nonlinearity. Our method can not only be used for two-photon hyperentangled Bell state analysis and three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analysis, but is also suitable for N -photon hyperentangled GHZ state analysis. In our protocols, the bit information of hyperentanglement is read out via the nonlinear interaction, and the phase information is obtained by using linear optical element and single photon detector. This approach is achievable with the current technology, and it will be useful for practical high-capacity quantum communication schemes.
We study Greenberger-Horne-Zeilinger--type (GHZ-type) and WWW-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 WWW-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate WWW-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 WWW-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.
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