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Physical Review A

Theory of the three-photon entangled state

Timothy E. Keller, Morton H. Rubin, Yanhua H. Shih, Ling-An Wu

Published Mar 1, 1998• 54 citations
Publisher

Abstract

Evaluation of the Greenberger-Horne-Zeilinger (GHZ) theory requires an entangled $n$-particle state with $n>~3$. To date, experimental achievement of a suitable GHZ state has proved elusive. This paper presents an approach to generate a three-photon entangled state and presents the theory of its space-time structure. Since an accurate picture of the space-time structure is important in understanding the two-photon state, an accurate picture of the three-photon state should be equally important.

DOI
10.1103/physreva.57.2076

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Evaluation of the Greenberger-Horne-Zeilinger (GHZ) theory requires an entangled nnn-particle state with n> 3n>~3n> 3. To date, experimental achievement of a suitable GHZ state has proved elusive. This paper presents an approach to generate a three-photon entangled state and presents the theory of its space-time structure. Since an accurate picture of the space-time structure is important in understanding the two-photon state, an accurate picture of the three-photon state should be equally important.
In tripartite discrete systems, two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the WWW class. To date, much research effort has been concentrated on the polarization entangled three-photon GHZ and WWW states. Most studies of continuous-variable multiparticle entanglement have been focused on Gaussian states. In this Brief Report, we examine two classes of three-photon entangled states in space and time. One class is a three-mode three-photon entangled state and the other is a two-mode triphoton state. These states show behavior similar to the GHZ and WWW states when one of the photons is not detected. The three-mode entangled state resembles a WWW state, while a two-mode three-photon state resembles a GHZ state when one of the photons is traced away. We characterize the distinction between these two states by comparing the second-order correlation functions G(2){G}^{(2)}G(2) with the third-order correlation function G(3){G}^{(3)}G(3).
The premises of the Einstein-Podolsky-Rosen argument for their claim that quantum mechanics is an incomplete theory are inconsistent when applied to three-particle systems in entangled Greenberger-Horne-Zeilinger states.However, thus far there is no experimental confirmation for existence of such states.We propose a technique to obtain Greenberger-Horne-Zeilinger states which rests upon an observation that when a single particle from two independent entangled pairs is detected in a manner such that it is impossible to determine from which pair the single came, the remaining three particles become entangled.
We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as Greenberger-Horne-Zeilinger (GHZ) states, play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes. Our experimental arrangement is such that we start with two pairs of entangled photons and register the photons in a way that any information as to which pair each photon belongs to is erased. After detecting a trigger photon, the registered events at the detectors for the remaining three photons exhibit the desired GHZ correlations.
This Letter reports the first experimental demonstration of Greenberger-Horne-Zeilinger (GHZ) entanglement swapping. We start with three pairs of entangled photons. Upon projection of three single photons, each from an entangled pair, into a GHZ state, the other three originally independent photons are entangled in a GHZ state-creation of multiparticle entanglement without any direct interaction. This scheme may facilitate networks for quantum telephone exchange, multiparty quantum communication and distributed quantum computation.
The first characterization of mixed-state entanglement was achieved for two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension concerns mixtures of a pure entangled state [such as the Greenberger-Horne-Zeilinger (GHZ) state] and the unpolarized state. These mixed states serve as benchmark for the robustness of multipartite entanglement. They share the symmetries of the GHZ state. We call such states GHZ symmetric. Here we give a complete description of the entanglement in the family of three-qubit GHZ-symmetric states and, in particular, of the three-qubit generalized Werner states. Our method relies on the appropriate parametrization of the states and on the invariance of entanglement properties under general local operations. An application is the definition of a symmetrization witness for the entanglement class of arbitrary three-qubit states.
We demonstrate how a new exactly soluble cavity QED model can be used to test local realism associated with three-particle entangled states, as proposed by Mermin. These states embody the correlations described by Greenberger, Horne, and Zeilinger (GHZ) and provide a stronger refutation of local hidden variable theories than is possible with Bell inequalities. It is shown that two photons distributed in the model’s four cavity modes coupled with a two-level atom can effectively produce three independent spin-1/2 particle states. We discuss preparation of the desired perfectly correlated GHZ state and a method to perform measurement on various field modes and atomic level correlations equivalent to a spin component along any direction.