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arXiv:2105.03709 · Physical Review A

Nonlocality sharing for a three-qubit system via multilateral sequential measurements

Changliang Ren, Xiaowei Liu, Wenlin Hou, Tianfeng Feng, Xiaoqi Zhou

Published May 25, 2022• 23 citations
arXivHTMLPDF

Abstract

Nonlocality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Nonlocality sharing based on the multiple violations of Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality in the trilateral sequential measurements scenario can be observed, where all of eight MABK inequalities can be violated simultaneously. Nevertheless, the genuine nonlocality sharing based on the multiple violation of Svetlichny inequality can be only observed in the unilateral sequential measurements scenario. Compared with two-qubit cases, the nonlocality sharing in a three-qubit system shows more fruitful characteristics.

DOI
10.1103/physreva.105.052221

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Nonlocality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Nonlocality sharing based on the multiple violations of Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality in the trilateral sequential measurements scenario can be observed, where all of eight MABK inequalities can be violated simultaneously. Nevertheless, the genuine nonlocality sharing based on the multiple violation of Svetlichny inequality can be only observed in the unilateral sequential measurements scenario. Compared with two-qubit cases, the nonlocality sharing in a three-qubit system shows more fruitful characteristics.
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.
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.
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.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of postmeasurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems [i.e., the double-chain setting, see S. M. Cheng et al., Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.
Benchmarking quantum processors is a central task in every roadmap aimed at quantum advantage. Here, we discuss a benchmarking protocol based on the violation of the Svetlichny inequality, which is designed to simulate genuine multipartite nonlocality. We compare it with Mermin's inequality, and present the results of applying this framework to two different quantum processing units -the superconducting system Garnet (from IQM) and the ion-trap system Marmot (from AQT), testing different families of quantum circuits for three to five qubits under identical experimental conditions. We also run simultaneous triplet tests across the full register, including a comparison between GHZ and linear cluster states, to probe how Svetlichny-inequality violations depend on qubit location and calibration. Our results demonstrate that tests based on genuine multipartite nonlocality provide a powerful tool to characterize the collective performance of quantum devices and to guide their calibration and optimization.