Integrability and Quantum Chaos in the Spectrum of Bell Operators

• URL: http://arxiv.org/abs/2406.11791v2
• Date: Tue, 29 Jul 2025 17:35:55 GMT
• Title: Integrability and Quantum Chaos in the Spectrum of Bell Operators
• Authors: Albert Aloy, Guillem Müller-Rigat, Maciej Lewenstein, Jordi Tura, Matteo Fadel,
• Abstract summary: We introduce a permutationally in multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and quantum chaos.<n>Surprisingly, we find that, in every irreducible representation exhibiting nonlocality, the measurement settings yielding maximal violation result in a Bell operator with Poissonian level statistics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a permutationally invariant multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and (lack of) quantum chaos. Interpreting the Bell operator, defined by fixing measurement settings, as an effective Hamiltonian, we analyze its spectral statistics across different SU(3) irreducible representations and measurement choices. Surprisingly, we find that, in every irreducible representation exhibiting nonlocality, the measurement settings yielding maximal violation result in a Bell operator with Poissonian level statistics, thus signaling integrable behavior. This integrability is both unique and fragile, since generic or slightly perturbed measurements lead to the Wigner-Dyson statistics associated with chaotic behavior. Through further analysis, we are able to identify an emergent parity symmetry in the Bell operator near the point of maximal violation, providing an explanation for the observed regularity in the spectrum. These results suggest a deep interplay between optimal quantum measurements, non-local correlations, and integrability, opening new perspectives at the intersection of Bell nonlocality and quantum chaos.

Related papers

• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Local models and Bell inequalities for the minimal triangle network [84.67234803583032]
  Nonlocal correlations enable surprising phenomena in quantum information and quantum foundations. We study one of the simplest scenarios, namely that of distributions invariant under permutations of parties in the minimal triangle network. We provide new insights on the existence of a classical-quantum gap in the triangle network with binary outcomes.
  arXiv  Detail & Related papers  (2025-03-20T19:11:06Z)
• Correlated Noise Estimation with Quantum Sensor Networks [18.51122677780099]
  We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks.<n>We identify a sensing protocol, reminiscent of a many-body echo sequence, that achieves the fundamental limits of measurement sensitivity for a broad class of problems.
  arXiv  Detail & Related papers  (2024-12-23T19:00:06Z)
• Nonlocality of Quantum States can be Transitive [0.0]
  We show that quantum steering already exhibits transitivity in a three-qubit setting. We also discuss connections between the problem of nonlocality transitivity and the largely overlooked polygamous nature of nonlocality.
  arXiv  Detail & Related papers  (2024-12-13T19:00:12Z)
• Nonlocality under Jaynes-Cummings evolution: beyond pseudospin operators [44.99833362998488]
  We re-visit the generation and evolution of (Bell) nonlocality in hybrid scenarios whose dynamics is determined by the Jaynes-Cummings Hamiltonian. Recent results on the optimal Bell violation in qubit-qudit systems show that the nonlocality is much greater than previously estimated.
  arXiv  Detail & Related papers  (2024-10-14T16:01:23Z)
• Effects of Topological Boundary Conditions on Bell Nonlocality [0.9374652839580183]
  Bell nonlocality is the resource that enables device-independent quantum information processing tasks. Our work can act as a guide to certify Bell nonlocality in many-qubit devices.
  arXiv  Detail & Related papers  (2024-05-23T13:58:50Z)
• Quantum Chaos in Random Ising Networks [36.136619420474766]
  Investigation of universal quantum chaotic signatures in the transverse field Ising model on an ErdHos-R'enyi network.<n>Level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks.
  arXiv  Detail & Related papers  (2024-05-23T09:50:59Z)
• Some consequences of Sica's approach to Bell's inequalities [55.2480439325792]
  Louis Sica derived Bell's inequalities from the hypothesis that the time series of outcomes observed in one station does not change if the setting in the other station is changed. In this paper, Sica's approach is extended to series with non ideal efficiency and to the actual time structure of experimental data.
  arXiv  Detail & Related papers  (2024-03-05T13:59:52Z)
• Bell correlations of a thermal fully-connected spin chain in a vicinity of a quantum critical point [0.0]
  Bell correlations are among the most exotic phenomena through which quantum mechanics manifests itself. Their presence signals that the system can violate the postulates of local realism. It is of growing interest to characterize the Bell content'' of complex, scalable many-body systems.
  arXiv  Detail & Related papers  (2024-03-04T19:00:01Z)
• Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms [22.554728415868574]
  We study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state in multipartite Bell scenarios. We exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of a Bell inequality.
  arXiv  Detail & Related papers  (2023-10-31T17:43:59Z)
• Bell inequalities with overlapping measurements [52.81011822909395]
  We study Bell inequalities where measurements of different parties can have overlap. This allows to accommodate problems in quantum information. The scenarios considered show an interesting behaviour with respect to Hilbert space dimension, overlap, and symmetry.
  arXiv  Detail & Related papers  (2023-03-03T18:11:05Z)
• Genuine Bell locality and nonlocality in the networks [0.0]
  Local hidden variables are strictly distributed in the specific observers rather than the whole ones. Moreors are involved in the proposed linear and non-linear Bell-type inequalities. How entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.
  arXiv  Detail & Related papers  (2022-09-23T04:23:16Z)
• Quantum correlations on the no-signaling boundary: self-testing and more [0.39146761527401425]
  We prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations. All correlations of $mathcalM$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements.
  arXiv  Detail & Related papers  (2022-07-28T01:55:21Z)
• Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
  We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
  arXiv  Detail & Related papers  (2022-03-30T18:00:00Z)
• Optimality of any pair of incompatible rank-one projective measurements for some non-trivial Bell inequality [0.0]
  Bell non-locality represents one of the most striking departures of quantum mechanics from classical physics. We show that for any pair of rank-one projective measurements, there exists a Bell inequality that is maximally violated by this pair. When investigating the robustness of these violations to noise, we demonstrate that the realization which is most robust to noise is not generated by MUBs.
  arXiv  Detail & Related papers  (2021-12-14T17:41:05Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Hybrid no-signaling-quantum correlations [0.2085467441379275]
  We introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term $textbfHNSQ$ in the multi-party Bell scenario. Specifically, the set $textbfHNSQ$ is a super-quantum set of correlations derived from no-signaling assemblages. In contrast to the usual no-signaling correlations, the new set allows for simple security of (one-sided)-device-independent applications against super-quantum adversaries.
  arXiv  Detail & Related papers  (2021-07-14T17:40:42Z)
• Exploring Bell nonlocality of quantum networks with stabilizing and logical operators [0.0]
  Knowing the stabilizing and logical operators indeed provides a new way of exploring Bell non-locality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. The tilted nonlinear Bell inequalities tailored for specific non-maximal entangled stabilizer states are also explored.
  arXiv  Detail & Related papers  (2021-05-09T05:13:41Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement [0.0]
  We investigate the simplest network, known as the bilocality scenario. We report noise-tolerant quantum correlations that elude bilocal variable models. We pave the way for an experimental realisation by presenting a simple two-qubit quantum circuit.
  arXiv  Detail & Related papers  (2020-06-30T11:32:26Z)
• Detecting many-body Bell non-locality by solving Ising models [0.0]
  We show that an arbitrary set of quantum data is compatible with a local theory, if not, it delivers a many-body Bell inequality violated by the quantum data. We use our approach to unveil new many-body Bell inequalities, violated by suitable measurements on paradigmatic quantum states.
  arXiv  Detail & Related papers  (2020-04-16T17:40:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.