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arXiv:quant-ph/0307097 · Physical Review A

Scheme for generating Greenberger-Horne-Zeilinger-type states ofnphotons

Yoav Sagi

Published Oct 20, 2003• 25 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.68.042320

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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.
We propose a scheme to probabilistically generate Greenberger-Horne-Zeilinger (GHZ) states encoded on the path degree of freedom of three photons. These photons are totally independent from each other, having no direct interaction during the whole evolution of the protocol, which remarkably requires only linear optical devices to work, and two extra ancillary photons to mediate the correlation. The efficacy of the method, which has potential application in distribited quantum computation and multiparty quantum communication, is analyzed in comparison with similar proposals reported in the recent literature. We also discuss the main error sources that limit the efficiency of the protocol in a real experiment and some interesting aspects about the mediator photons in connection with the concept of spatial nonlocality.
High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this Letter, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the d-level N-partite Greenberger-Horne-Zeilinger (GHZ) state with single-photon sources and linear operations. Our scheme requires dN photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beam splitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.
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.