Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.17551 · Quantum Information Processing

Sharing tripartite nonlocality sequentially using only projective measurements

Yiyang Xu, Hao Sun, Fen-Zhuo Guo, Haifeng Dong, Qiaoyan Wen

Published Jan 10, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlocal correlations. Previous work has accomplished sequential tripartite nonlocality sharing through unsharp measurements. In this paper, we investigate the sharing of tripartite nonlocality using only projective measurements and sharing classical randomness. For the generalized GHZ state, we have demonstrated that using unbiased measurement choices, two Charlies can share the standard tripartite nonlocality with a single Alice and a single Bob, while at most one Charlie can share the genuine tripartite nonlocality with a single Alice and a single Bob. However, with biased measurement choices, the number of Charlies sharing the genuine tripartite nonlocality can be increased to two. Nonetheless, we find that using biased measurements does not increase the number of sequential observers sharing the standard tripartite nonlocality. Moreover, we provide the feasible range of double violation for the parameters of the measurement combination probability with respect to the state.

DOI
10.1007/s11128-024-04638-w

Related papers

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

XI Ya, Zheng, Zhu-Jun

There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob.

arXiv:2207.00296•Jul 1, 2022•1 citation

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

Ya Xi, Mao-Sheng Li, Libin Fu +1 more

Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.

Physical Review A•Jun 22, 2023•17 citations

Sequential Sharing of Quantum Nonlocality via Projective Measurements

Bingzi Huo, Kunkun Wang, Dengke Qu +6 more

Sequential sharing of quantum nonlocality enables multiparty collaborative information processing, which is typically realized through unsharp measurements in previous studies. By contrast, we experimentally demonstrate that the sequential sharing of quantum nonlocality can be observed using only projective measurements, with the introduction of classical randomness. We achieve sequential violations of the Clauser-Horne-Shimony-Holt inequality in a bipartite quantum system by sharing classical randomness or using a probabilistic projective measurement. Extending the first protocol to a tripartite quantum system, sequential tripartite nonlocality is observed with the Greenberger-Horne-Zeilinger state, where violations of the Mermin inequality are observed in sequential measurements. We experimentally demonstrate these phenomena through the preparation and measurement of a three-photon entangled state. Our work reveals the key role of projective measurements in the sequential sharing of quantum nonlocality, providing a new experimental complement for measuring quantum nonlocality and opening new technological pathways for distributed utilization nonlocality in quantum networks.

Physical Review Letters•Feb 20, 2026•2 citations

Experimental sharing of Bell nonlocality with projective measurements

Ya Xiao, Yan-Xin Rong, Shuo Wang +3 more

Abstract In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.

New Journal of Physics•May 1, 2024•9 citations

Unbounded Sharing of Nonlocality Using Qubit Projective Measurements

Satyaki Sasmal, Som Kanjilal, A. K. Pan

The prevailing consensus is that the sequential sharing of nonlocality in a Bell experiment requires generalized unsharp measurements, given that a sharp measurement inevitably destroys the entanglement of the shared state. In contrast, a recent work [A. Steffinlongo and A. Tavakoli, Projective measurements are sufficient for recycling nonlocality, Phys. Rev. Lett. 129, 230402 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.230402] demonstrated the sharing of nonlocality up to two sequential observers by employing projective measurement aided with local randomness. Here, we introduce a form of local randomness-assisted qubit projective measurement protocol that enables the sharing of nonlocality by an arbitrary number of sequential observers (Bobs) with a single spatially separated observer (Alice). We achieve this by inspecting the diversity involved in implementing generalized measurements that harness nonlocality by preserving a sufficient amount of entanglement of the shared two-qubit entangled state. Furthermore, we highlight the crucial interplay between the degrees of measurement incompatibility of Alice and Bob in demonstrating the unbounded sharing of nonlocality.

arXiv:2311.07977•Physical Review Letters•Oct 22, 2024•13 citations

Sharing Bell nonlocality of bipartite high-dimensional pure states using only projective measurements

Tinggui Zhang, Hong Wei Yang, Shao-Ming Fei

Bell nonlocality is the key quantum resource in some device-independent quantum information processing. It is of great importance to study the efficient sharing of this resource. Unsharp measurements are widely used in sharing the nonlocality of an entangled state shared among several sequential observers. Recently, the authors in [Phys. Rev. Lett. 129, 230402 (2022)] showed that the Bell nonlocality of two-qubit pure states can be shared even when one only uses projective measurements and local randomness. We demonstrate that projective measurements are also sufficient for sharing the Bell nonlocality of arbitrary high-dimensional pure bipartite states. Our results promote further understanding of the nonlocality sharing of high-dimensional quantum states under projective measurements.

arXiv:2402.12614•Physical Review A•Feb 13, 2024•9 citations
Abstract Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlocal correlations. Previous work has accomplished sequential tripartite nonlocality sharing through unsharp measurements. In this paper, we investigate the sharing of tripartite nonlocality using only projective measurements and sharing classical randomness. For the generalized GHZ state, we have demonstrated that using unbiased measurement choices, two Charlies can share the standard tripartite nonlocality with a single Alice and a single Bob, while at most one Charlie can share the genuine tripartite nonlocality with a single Alice and a single Bob. However, with biased measurement choices, the number of Charlies sharing the genuine tripartite nonlocality can be increased to two. Nonetheless, we find that using biased measurements does not increase the number of sequential observers sharing the standard tripartite nonlocality. Moreover, we provide the feasible range of double violation for the parameters of the measurement combination probability with respect to the state.
There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob.
Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.
Sequential sharing of quantum nonlocality enables multiparty collaborative information processing, which is typically realized through unsharp measurements in previous studies. By contrast, we experimentally demonstrate that the sequential sharing of quantum nonlocality can be observed using only projective measurements, with the introduction of classical randomness. We achieve sequential violations of the Clauser-Horne-Shimony-Holt inequality in a bipartite quantum system by sharing classical randomness or using a probabilistic projective measurement. Extending the first protocol to a tripartite quantum system, sequential tripartite nonlocality is observed with the Greenberger-Horne-Zeilinger state, where violations of the Mermin inequality are observed in sequential measurements. We experimentally demonstrate these phenomena through the preparation and measurement of a three-photon entangled state. Our work reveals the key role of projective measurements in the sequential sharing of quantum nonlocality, providing a new experimental complement for measuring quantum nonlocality and opening new technological pathways for distributed utilization nonlocality in quantum networks.
Abstract In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.
The prevailing consensus is that the sequential sharing of nonlocality in a Bell experiment requires generalized unsharp measurements, given that a sharp measurement inevitably destroys the entanglement of the shared state. In contrast, a recent work [A. Steffinlongo and A. Tavakoli, Projective measurements are sufficient for recycling nonlocality, Phys. Rev. Lett. 129, 230402 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.230402] demonstrated the sharing of nonlocality up to two sequential observers by employing projective measurement aided with local randomness. Here, we introduce a form of local randomness-assisted qubit projective measurement protocol that enables the sharing of nonlocality by an arbitrary number of sequential observers (Bobs) with a single spatially separated observer (Alice). We achieve this by inspecting the diversity involved in implementing generalized measurements that harness nonlocality by preserving a sufficient amount of entanglement of the shared two-qubit entangled state. Furthermore, we highlight the crucial interplay between the degrees of measurement incompatibility of Alice and Bob in demonstrating the unbounded sharing of nonlocality.
Bell nonlocality is the key quantum resource in some device-independent quantum information processing. It is of great importance to study the efficient sharing of this resource. Unsharp measurements are widely used in sharing the nonlocality of an entangled state shared among several sequential observers. Recently, the authors in [Phys. Rev. Lett. 129, 230402 (2022)] showed that the Bell nonlocality of two-qubit pure states can be shared even when one only uses projective measurements and local randomness. We demonstrate that projective measurements are also sufficient for sharing the Bell nonlocality of arbitrary high-dimensional pure bipartite states. Our results promote further understanding of the nonlocality sharing of high-dimensional quantum states under projective measurements.