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Chinese Physics B

An experimental proposal certification for any three-qubit generalized Greenberger–Horne–Zeilinger states based on fine-grained steering inequality

Zhihao Bian, Jia-Qi 佳琪 Sun 孙, Yi 毅 Shen 沈

Published Sep 26, 2025• 0 citations
Publisher

Abstract

Abstract Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) state based on the fine-grained steering inequality was proved [ Quantum Studies: Mathematics and Foundations 9 175 (2022)]. Here we provide an experimental proposal to prepare the GGHZ state in a photon system. The measurement observables in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experimental proposal can observe the maximum quantum violation for any three-qubit GGHZ state. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.

DOI
10.1088/1674-1056/ae0bfd

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•Apr 9, 2020•0 citations
Abstract Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) state based on the fine-grained steering inequality was proved [ Quantum Studies: Mathematics and Foundations 9 175 (2022)]. Here we provide an experimental proposal to prepare the GGHZ state in a photon system. The measurement observables in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experimental proposal can observe the maximum quantum violation for any three-qubit GGHZ state. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.
Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states based on the fine-grained steering inequality was proved [Quantum Studies: Mathematics and Foundations, 2022, 9(2): 175-198]. Here we provide an experimental proposal to prepare the GGHZ states in photon system. The measurement observalbes in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experiment proposal can observe the maximum quantum violation for any three-qubit GGHZ states. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.
As stated by S. Ghose et al. [Phys. Rev. Lett. 102, 250404 (2009)], there are certain relationships between tripartite entanglement and tripartite nonlocality for three-qubit Greenberger-Horne-Zeilinger (GHZ) class states. In the present work, we have experimentally demonstrated the theoretical results of Ghose et al. by using both three-photon generalized GHZ (GGHZ) states and maximal slice (MS) states with a count of $\ensuremath{\sim}$10/s. From the data, we have verified the agreement of the experimental violation of the Svetlichny inequality with the one predicted by quantum mechanics given the reconstructed density matrix. For the MS states, it is demonstrated that the amount of violation increases linearly following the increase of the degree of tripartite entanglement. In contrast, for GGHZ states, there is a minimal value of the violation when the degree of tripartite entanglement is 1/3. Both of the results are consist with the theoretical prediction.
We aim to explore all possible scenarios of (1 → 2) (where one wing is untrusted and the others two wings are trusted) and (2 → 1) (where two wings are untrusted, and one wing is trusted) genuine tripartite Einstein–Podolsky–Rosen (EPR) steering. The generalized Greenberger–Horne–Zeilinger (GHZ) state is shared between three spatially separated parties, Alice, Bob and Charlie. In both (1 → 2) and (2 → 1), we discuss the untrusted party and trusted party performing a sequence of unsharp measurements, respectively. For each scenario, we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality. The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters. Moreover, both the sharpness parameters range and the state parameters range in the scenario of (1 → 2) steering are larger than those in the scenario of (2 → 1) steering.
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 $19\ensuremath{\sigma}$.
Abstract A theoretical proposal for the complete analysis of high-dimensional Greenberger–Horne–Zeilinger (GHZ) state is presented in this Letter. We first demonstrate the approach for the complete three-photon GHZ state measurement in three dimensions, and then generalize it to the situation of N-photon system in d dimensions. In our approach, the photonic hyperentanglement and quantum Fourier transform are both utilized. The presented proposal will be useful for the high-dimensional multi-photon quantum computation and quantum communication.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the earliest paradoxes, arising from the lack of local realistic description of mechanics. The EPR paradox leads to the important concept of quantum which manifests itself by three different phenomena: entanglement, steering, and Bell's nonlocality. Two well-known paradoxes related to Bell's nonlocality, i.e. the Greenberger-Horne-Zeilinger paradox and the Hardy paradox, have been widely studied and also experimentally confirmed. However, an experimental test of the EPR paradox is still lacking. The EPR paradox is essentially a steering paradox, and recently it has been mathematically formulated as a contradiction equality k=1k=1k=1, thus making it amenable to an experimental verification. Moreover, based on the EPR paradox we also derive a generalized linear steering inequality. In this work, we perform the first experimental test of the EPR paradox in a two-qubit scenario, and also verify the corresponding generalized steering inequality, which has an advantage over the usual one by detecting more steerability of states. Experimental results confirm the theoretical predictions within the experimental errors, and provide a deeper understanding of foundation.