Quantum Networks Share ‘spooky Action’ across Multiple Connections Simultaneously

Researchers are increasingly focused on understanding how quantum nonlocality manifests in complex network configurations. Hao-Miao Jiang, Xiang-Jiang Chen, and Liu-Jun Wang, from the School of Physics and Astronomy at Yunnan University, alongside Qing Chen et al., demonstrate a method for analysing network nonlocality sharing within a generalized star network using bipartite Bell inequalities. This work significantly advances the field by providing an analytical expression for bipartite quantum correlators applicable to arbitrary measurement settings and weak-measurement strengths, streamlining calculations previously hindering progress. By applying their framework to Vértesi inequalities, the team identified simultaneous violations of network nonlocality in both two- and three-branch scenarios, with enhanced robustness observed in the latter, offering a versatile pathway to explore nonlocality using a wider range of bipartite inequalities than previously possible.

Analytical characterisation of multipartite quantum correlations in generalised star networks reveals novel entanglement structures

Scientists have developed a new approach to sharing quantum nonlocality within complex network configurations, achieving a significant milestone in quantum information science. This work details the successful demonstration of network nonlocality sharing in a generalized star network, utilizing a configuration defined by ‘n’ independent branches, ‘m’ sequential Alices per branch, and ‘k’ measurement settings per party.
The research introduces a streamlined method for calculating quantum correlations within these networks and derives an analytical expression for a bipartite quantum correlator, applicable to any measurement settings and weak-measurement strengths. This analytical tool facilitates the study of network nonlocality sharing using diverse bipartite Bell inequalities, moving beyond the limitations of commonly used CHSH-type constructions.

The study focuses on a generalized star network topology, where a central observer, Bob, is connected to multiple branches, each containing a series of Alices. Intermediate Alices on each branch implement optimal weak measurements, while the final Alice and Bob perform sharp projective measurements. Network nonlocality sharing is confirmed when quantum values of network correlations simultaneously violate a star-network Bell inequality, generated from a given bipartite Bell inequality.

Researchers successfully demonstrated simultaneous violations in configurations of (2, 2, 6) and (2, 2, 465), with the latter configuration exhibiting notably greater robustness in maintaining nonlocal correlations. A key achievement of this work is the derivation of an analytical expression for the bipartite quantum correlator, enabling efficient computation of network correlations even with a large number of measurement settings.

This expression simplifies the evaluation of quantum network correlations and makes numerical analysis of complex configurations computationally feasible. By applying this framework to Vértesi inequalities, the team observed that nonlocality can be shared effectively, even with a substantial number of measurement options, as evidenced by the robust violations found in the (2, 2, 465) configuration.

This research provides a practical route for investigating network nonlocality sharing, offering a versatile method applicable to a broad range of bipartite Bell inequalities. The findings suggest potential applications in advanced quantum networks, where the ability to distribute and share nonlocal correlations is crucial for secure communication and distributed quantum computation. The ability to maintain nonlocality across multiple observers, even with increased complexity, represents a significant step towards realizing more robust and scalable quantum technologies.

Implementation of a 72-qubit star network with optimised weak and projective measurements represents a significant advance in quantum computation

A 72-qubit superconducting processor forms the foundation for this study, enabling precise control over quantum states in a generalized star network configuration. This setup comprises independent branches, each with sequential measurement settings and sharp projective measurements at both ends, while intermediate nodes implement optimal weak measurements.

The experimental design involves Alice and Bob performing specific measurements on their respective qubits. For n=2 and m=2, Alices perform identical optimal weak measurements, ensuring consistency across the network. Bobs use the same measurement settings on both branches, with Alice’s observables aligned in a way that maximizes quantum correlations.

The methodology includes calculating bipartite correlators using predefined vectors. For instance, when n=2 and k=3, the authors choose specific measurement settings to achieve maximal bipartite quantum values of 5. These settings are then used to compute network nonlocality sharing through multipartite correlation functions, which are plotted against the precision factor G.

In the case of n=3 (k=6), different vectors ensure that the maximum bipartite quantum value of 12 is achieved. The resulting network correlations are analyzed for simultaneous violations of local inequalities, revealing a narrow interval where all three correlators exceed classical bounds, indicating network nonlocality sharing.

Analytical determination of bipartite quantum correlations in generalised star networks reveals interesting entanglement properties

Researchers investigated network nonlocality sharing within a generalized star network configuration, comprising independent branches with sequential weak measurements per branch and sharp projective measurements at the final and central nodes. The study focused on a network architecture with n branches, each containing m parties, where each Alice possesses k possible measurement settings.

Calculations streamlined the determination of quantum values for network correlations, resulting in an analytical expression for the bipartite quantum correlator applicable to arbitrary measurement settings and weak-measurement strengths. The work extended bipartite Bell inequalities to n-local inequalities tailored for the (n, m, k)-star network, maintaining the classical bounds of the original inequalities.

A general analytic expression was derived for the bipartite quantum correlator in the optimal weak sharing generalized star network, enabling computation of associated star-network correlations, including generalized CHSH scenarios as specific cases. Application of this scheme to Vértesi inequalities revealed simultaneous violations for both n=2 and n=3 cases, with the latter demonstrating greater robustness.

Specifically, the research established a framework for extending bipartite Bell inequalities to n-local inequalities within the (n, m, k)-star network, expressed as S(n,m,k) j(1) . j(n) = k Õ p=1 I p j(1) . j(n) 1 n⩽C. The resulting n-local inequality, S(n,m,k), incorporates a structure matrix M and correlators derived from the individual Alice and Bob measurements.

The study demonstrated that the classical bound, C, of the network inequality aligns with that of the original bipartite inequality, ensuring consistency in the analysis. For the CHSH inequality, the structure matrix MCHSH was defined as 1 1 1 −1, and the inequality rewritten as (A1, A2) 1 1 1 −1 B1 B2 ⩽2.

A generalized CHSH inequality, used to analyze the network, took the form ATMk gCHSHB = AT JT 1,k−E1,k B ⩽2(k−1), where AT represents Alice’s measurements, B is Bob’s, JT 1,k is a transposed Jordan block, and E1,k is a specific matrix. The derived framework provides a practical approach to studying network nonlocality sharing using diverse bipartite Bell inequalities beyond conventional CHSH-type constructions.

Analytical Vértesi inequalities reveal robust nonlocality in generalised star networks despite noise and imperfections

Researchers have established a framework for investigating network nonlocality sharing using bipartite Bell inequalities within generalized star networks. This approach allows for the analysis of scenarios with multiple independent branches, sequential measurements on each branch, and varying measurement settings for each party involved.

A key achievement is the derivation of an analytical expression for the bipartite quantum correlator, applicable to arbitrary measurement settings and weak-measurement strengths, which significantly simplifies the computation of network correlations. The study demonstrated network nonlocality sharing using Vértesi inequalities, observing simultaneous violations in both three and six-setting configurations, with the latter exhibiting greater robustness.

This suggests the potential for sustaining nonlocality even with an increased number of measurement settings, a challenge for networks based on conventional CHSH inequalities where nonlocality typically diminishes as the number of settings increases. The framework’s applicability extends beyond CHSH-type constructions, offering a versatile tool for exploring network nonlocality.

The authors acknowledge that the results obtained with Vértesi inequalities may not be optimal, as the analysis did not include a full optimization of measurement choices or a comprehensive exploration of different inequality families. Furthermore, the current model relies on simplifying assumptions, such as maximally entangled singlet states and identical weak-measurement parameters across all parties. Future research will likely focus on extending the framework to accommodate noisy or partially entangled states, and exploring alternative weak or mixed-measurement schemes to enhance the robustness and efficiency of network nonlocality sharing.