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arXiv:2412.19028

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

Zhihao Bian, Sun, Jia-Qi, Yi Shen

Published Dec 26, 2024• 0 citations
arXivHTMLPDF

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) 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.

DOI
10.48550/arxiv.2412.19028

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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.
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.
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.
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 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 One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.
The [Formula: see text]-qubit Greenberger–Horne–Zeilinger (GHZ) states are the maximally entangled states of [Formula: see text] qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser–Horne–Shimony–Holt (CHSH) inequality, we show that the [Formula: see text]-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any [Formula: see text]-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality in which the maximal violation of Bell’s inequality can be robust under some specific noises adding to the [Formula: see text]-qubit GHZ states.