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Physical Review Letters

Experimental Realization of a Three-Qubit Entangled W State

Manfred Eibl, Nikolai Kiesel, Mohamed Bourennane, Christian Kurtsiefer, Harald Weinfurter

Published Feb 18, 2004• 362 citations
Publisher

Abstract

We report on the experimental observation of the three-photon polarization-entangled W state using spontaneous parametric down-conversion. This state is inequivalent to the Greenberger-Horne-Zeilinger state under stochastic local operations and classical communications and thus is the representative of the second class of genuine tripartite entanglement. We study the characteristic features of entanglement and demonstrate the high degree of two-photon entanglement in the W state.

DOI
10.1103/physrevlett.92.077901

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We report on the experimental observation of the three-photon polarization-entangled W state using spontaneous parametric down-conversion. This state is inequivalent to the Greenberger-Horne-Zeilinger state under stochastic local operations and classical communications and thus is the representative of the second class of genuine tripartite entanglement. We study the characteristic features of entanglement and demonstrate the high degree of two-photon entanglement in the W state.
Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. For entangled three-qubit states it has been shown that there are two inequivalent classes of states, under stochastic local operations and classical communications. The classes are represented by the GHZ- and W-state. The GHZ-state has been used to prove Bell's theorem without inequality. Contrary to the GHZ-state, the W-state shows high robustness of entanglement against photon loss. Here we show the first experimental results on the observation of the polarization entangled three-photon W-state from spontaneous parametric down-conversion.
Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the WWW state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal NNN-qubit GHZ state to a state arbitrarily close to the ideal NNN-qubit WWW state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.
We present the experimental observation of the symmetric four-photon entangled Dicke state with two excitations |D_{4};{(2)}. A simple experimental setup allowed quantum state tomography yielding a fidelity as high as 0.844+/-0.008. We study the entanglement persistency of the state using novel witness operators and focus on the demonstration of a remarkable property: depending on the orientation of a measurement on one photon, the remaining three photons are projected into both inequivalent classes of genuine tripartite entanglement, the Greenberger-Horne-Zeilinger and W class. Furthermore, we discuss possible applications of |D_{4};{(2)} in quantum communication.
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the Greenberger-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher-dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.
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 states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely, the Greenberger-Horne-Zeilinger (GHZ) type and the WWW type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard WWW states, under the local measurement operations carried out by a single party and ppp (p=2,3p=2,3p=2,3) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.