A Geometric Family of Correlations Containing the Quantum Singlet

• URL: http://arxiv.org/abs/2606.12045v1
• Date: Wed, 10 Jun 2026 13:09:30 GMT
• Title: A Geometric Family of Correlations Containing the Quantum Singlet
• Abstract summary: We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function.<n>Results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function, within which the quantum singlet correlation appears as a particular member. Exact expressions for the correlation function are derived. Several structural results are established, including admissibility conditions, symmetry properties, a universal stationary point of the associated CHSH function, and an exact relation between the CHSH value at $ν=π/4$ and a geometric contrast measure defined on the underlying hidden-variable distributions. Rather than treating the quantum singlet correlation as an isolated target to be reproduced, the present framework places it within a broader geometric structure of correlations. These results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.

Related papers

• Learning the generating functional for variance reduction in lattice QCD [43.67714876032719]
  We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators.<n>We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework.
  arXiv  Detail & Related papers  (2026-06-14T19:24:19Z)
• Curvature-Guided Geometric Representation for Protein-Ligand Binding Affinity Prediction [38.825664822163816]
  RicciBind is a representation framework that integrates curvature-guided hierarchical structure learning with optimal transport (OT)-based cross-domain alignment.<n>Our experiments demonstrate that RicciBind achieved superior predictive performance and generalization across PLA benchmarks and virtual screening tasks.
  arXiv  Detail & Related papers  (2026-06-12T06:33:55Z)
• Quantum average correlations and complementarity relations via metric-adjusted skew information [21.984140030239583]
  We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information.<n>By defining measures of wave and particle features via metric-adjusted skew information, we establish complementarity relations among wave and particle features, quantum entropy, and average correlation.
  arXiv  Detail & Related papers  (2026-04-26T02:38:29Z)
• Localization Tensor Revisited: Geometric-Probabilistic Foundations and a Structure-Factor Criterion under Periodic Boundaries [2.5694382720775306]
  We revisit the localization tensor (LT) from geometric and probabilistic perspectives.<n>We identify the diagonal part, Cpp, as a "localization function" C(p), whose small-momentum behavior determines the LT in the thermodynamic limit.<n>We show that the finite-momentum behavior of C(p), together with an inverse participation ratio (IPR)-based upper bound valid in localized phases, provides a sharp criterion that discriminates localization from dimerization.
  arXiv  Detail & Related papers  (2026-02-16T14:29:57Z)
• Quantum correlations curvature, memory functions, and fundamental bounds [51.85131234265026]
  We show that quantum geometry can qualitatively modify the imaginary-time decay of correlations, leading to nontrivial curvature behavior.<n>More generally, we show a universal bound on correlation curvature that holds for interacting systems in thermal equilibrium.
  arXiv  Detail & Related papers  (2025-12-22T01:33:11Z)
• Flock: A Knowledge Graph Foundation Model via Learning on Random Walks [26.568227939080703]
  We study the problem of zero-shot link prediction on knowledge graphs (KGs)<n>We present Flock, a KGFM that iteratively samples random walks, encodes them into sequences via a recording protocol, embeds them with a sequence model, and aggregates representations of nodes and relations via learned pooling.<n>Flock perfectly solves our new diagnostic dataset Petals where current KGFMs fail, and achieves state-of-the-art performances on entity- and relation prediction tasks on 54 KGs from diverse domains.
  arXiv  Detail & Related papers  (2025-10-01T23:09:46Z)
• Evolution of multi-qubit correlations driven by mutual interactions [49.1574468325115]
  We analyze the evolution of the correlation tensor elements of quantum systems composed of $frac12$-spins.<n>We show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.
  arXiv  Detail & Related papers  (2025-07-01T11:45:08Z)
• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• Trade-off relations of geometric coherence [0.43512163406552007]
  We study the trade-off relation of geometric coherence in qubit systems. We derive the quantum uncertainty relations of the geometric coherence on two and three general measurement bases.
  arXiv  Detail & Related papers  (2023-10-24T03:04:59Z)
• Correlations of quantum curvature and variance of Chern numbers [0.0]
  We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations.
  arXiv  Detail & Related papers  (2020-12-07T18:00:40Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Multipartite Optimized Correlation Measures and Holography [8.594140167290098]
  We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. We present a procedure to derive such quantities, and construct a menagerie of symmetric optimized correlation measures on three parties. Some correlation measures vanish only on product states, and thus quantify both classical and quantum correlations. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces.
  arXiv  Detail & Related papers  (2020-07-22T18:00:01Z)
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case [0.0]
  We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit. We incidentally point out a possible interpretation of the Q-SSEP correlation functions via a surprising conneatorics and the associahedron polytopes.
  arXiv  Detail & Related papers  (2020-06-22T13:20:40Z)

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.