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arXiv:2303.08297 · Advanced Quantum Technologies

Violation of Bell Inequality by Four‐Photon Greenberger‐Horne‐Zeilinger State with a Phase from a Warm Atomic Ensemble

Jiho Park, Junghee Ryu, Heonoh Kim, Han Seb Moon

Published Aug 16, 2023• 3 citations
arXivHTMLPDF

Abstract

Abstract A Greenberger–Horne–Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, it is reported that the violations of the general Bell inequality (GBI) introduced in using the four‐photon polarization‐entangled phase‐GHZ state realized via intrinsic polarization correlation and collective two‐photon coherence in the 5S 1/2 –5P 3/2 –5D 5/2 transition of 87 Rb atoms. The phase‐GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the π/4 phase affords maximal violation of the GBI of 2√2 at the local measurement settings of the Pauli operators σ x and σ y . Strong violations of the GBI of the phase‐GHZ state by 47 standard deviations are experimentally demonstrated. In addition to the entanglement witness for the phase‐GHZ state, the results represent a genuine four‐photon entanglement of the phase‐GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic‐state distillation from entangled states, and quantum networks based on atom–photon interactions.

DOI
10.1002/qute.202300190

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Abstract A Greenberger–Horne–Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, it is reported that the violations of the general Bell inequality (GBI) introduced in using the four‐photon polarization‐entangled phase‐GHZ state realized via intrinsic polarization correlation and collective two‐photon coherence in the 5S 1/2 –5P 3/2 –5D 5/2 transition of 87 Rb atoms. The phase‐GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the π/4 phase affords maximal violation of the GBI of 2√2 at the local measurement settings of the Pauli operators σ x and σ y . Strong violations of the GBI of the phase‐GHZ state by 47 standard deviations are experimentally demonstrated. In addition to the entanglement witness for the phase‐GHZ state, the results represent a genuine four‐photon entanglement of the phase‐GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic‐state distillation from entangled states, and quantum networks based on atom–photon interactions.
Abstract Bright, entangled multiphoton sources based on atom–photon interactions are an essential requirement in the realization of several quantum information and quantum computation schemes based on photonic quantum systems. Here, a four‐photon polarization‐entangled Greenberger–Horne–Zeilinger (GHZ) state obtained from Doppler‐broadened atomic ensembles of 87 Rb atoms is experimentally demonstrated. Owing to collective two‐photon coherence in the Doppler‐broadened cascade‐type atomic system, the setup enables the generation of robust four‐photon GHZ states with a fidelity of 82.1% and a measured four‐photon average coincidence rate of 0.58 s −1 . It is believed that the generation of such bright and stable multiphoton GHZ states from atomic media is an important step toward realizing photonic quantum computation and practical quantum networks based on atom–photon interactions.
We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.
Abstract The realization of high-quality and stable entangled states is crucial for the advancement of quantum information science and technology. The entangled photons generated from a warm atomic ensemble exhibit high spectral purity and indistinguishability, offering significant potential for atom–photon-based quantum networks. We report high-quality time–frequency entangled continuous-wave (CW) photon pairs via a spontaneous four-wave mixing process in the cascade-type atomic transition of 5S 1/2 –5P 3/2 –5D 5/2 from a warm 87 Rb atomic ensemble. We observed Franson interference with the visibility of 99.6(8) % using two independent Franson interferometers, obtained by post-selecting the temporally indistinguishable two-photon events. The interferometer phases were actively stabilized using the reference laser frequency-locked to the 133 Cs (6S 1/2 -6P 3/2 ) transition. Beyond stabilizing the interferometers, the active control of these phases allowed us to measure the CHSH S -value directly and achieve a near-maximal Bell inequality violation with S = 2.83(7). This result demonstrates that warm atomic ensembles can serve as bright sources of time–frequency entanglement, which combined with active interferometer stabilization enable stable high-visibility operation for practical applications in quantum network.
We report the stable generation of a bright four-photon polarization-entangled Greenberger–Horne–Zeilinger (GHZ) state obtained by the spatial multiplexing of inherently polarization-entangled photons from a warm atomic ensemble of 87Rb. Owing to the total angular momentum conservation of the atomic state in the spontaneous four-wave mixing process of a cascade-type atomic system, the polarizations of the signal and idler photons in the two-photon decay are entangled. With a Rb vapor cell, we realize the generation of robust and bright four-photon GHZ states using two symmetrical spatial modes of inherently polarization-entangled photon pairs without applying an interferometric configuration. The four-photon average coincidence rate of the GHZ state with a fidelity of 0.88(2) is measured as 1.69(7) Hz under a weak pump power of 10 μW. The minimum Allan variance for the stability of the four-photon GHZ state is estimated as 0.92° for an average time of 10 h.
Abstract Since it was revealed that there are certain bipartite entangled states whose violations of Clauser–Horne–Shimony–Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs (Brown et al 2020 Phys. Rev. Lett. 125 090401), there are a series of analogs not only for bipartite systems but also for multipartite systems. For four-partite Greenberger-Horne-Zeilinger (GHZ) states, we construct a set of specific observables such that the quantum value of the Bell operator introduced in Zukowski and Brukner (2002 Phys. Rev. Lett. 88 210401) can be obtained analytically. Then, it is revealed that four-partite GHZ states can share numerous sequential non-localities by violating the corresponding Bell inequality.
The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by $7\ensuremath{\sigma}$. The fidelity of the GHZ state was around 8181%81, and an entanglement witness reveals a violation of the separability threshold by $19\ensuremath{\sigma}$.