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arXiv:quant-ph/0402198

Comment on "Experimental realization of a three-qubit entangled W state"

Jose Luis Cereceda

Published Feb 26, 2004• 0 citations
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Abstract

Recently Eibl et al. [PRL 92, 077901 (2004)] reported the experimental observation of the three-photon polarization-entangled W state. In this Comment we point out that, actually, the particular measurements involved in the experiment testing Mermin's inequality cannot be used for the verification of the existence of genuinely quantal tripartite correlations in the observed state, and therefore this state cannot conclusively be identified with the W state.

DOI
10.48550/arxiv.quant-ph/0402198

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Recently Eibl et al. [PRL 92, 077901 (2004)] reported the experimental observation of the three-photon polarization-entangled W state. In this Comment we point out that, actually, the particular measurements involved in the experiment testing Mermin's inequality cannot be used for the verification of the existence of genuinely quantal tripartite correlations in the observed state, and therefore this state cannot conclusively be identified with the W state.
A recent paper [] presented a bound for the three-qubit Mermin inequality such that the violation of this bound indicates genuine three-qubit entanglement. We show that this bound can be improved for a specific choice of observables. In particular, if spin observables corresponding to orthogonal directions are measured at the qubits (e.g., XXX and YYY spin coordinates), then the bound is the same as the bound for states with a local hidden variable model. As a consequence, it can straightforwardly be shown that in the experiment described by ], genuine three-qubit entanglement was detected.
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.
It is known that the violation of Svetlichny's inequality (SI), rather than the usual Mermin's inequality (MI), is a robust criterion to confirm the existence of genuine multipartite quantum nonlocality. In this paper, we propose a feasible approach to test SI with three two-level atoms (TLAs) dispersively coupled to a driven cavity. The proposal is based on the joint measurements of the states of three TLAs by probing the steady-state transmission spectra of the driven cavity: each peak marks one of the computational basis states and its relative height corresponds to the probability superposed in the detected three-TLA state. With these kinds of joint measurements, the correlation functions in SI can be directly calculated, and thus the SI can be efficiently tested for typical tripartite entanglement, i.e., genuine tripartite entanglement [e.g., Greenberger-Horne-Zeilinger (GHZ) and W states] and biseparable three-qubit entangled states (e.g., ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$). Our numerical experiments show that the SI is violated only by three-qubit GHZ and W states, not by biseparable three-qubit entangled state ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$, while the MI can still be violated by biseparable three-qubit entangled states. Thus the violation of SI can be regarded as a robust criterion for the existence of genuine tripartite entanglement.
Using spectral joint measurements of the qubits, we propose a scheme to test the tripartite Mermin inequality with three qubits dispersively coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then spectral joint measurements are introduced to directly confirm such tripartite entanglement. Assisted by a series of single-qubit operations, these measurements are further utilized to test the Mermin inequality. The feasibility of the proposal is robustly demonstrated by the present numerical experiments.