A Multi Affine Geometric Framework for Quantum Nonlocality. Unifying Berry Phases, Entanglement, and Coherence

• URL: http://arxiv.org/abs/2503.17995v1
• Date: Wed, 05 Mar 2025 19:34:58 GMT
• Title: A Multi Affine Geometric Framework for Quantum Nonlocality. Unifying Berry Phases, Entanglement, and Coherence
• Authors: Shoshauna Gauvin,
• Abstract summary: We develop a multi affine geometric framework to unify classical and quantum mechanical laws.<n>We show that divergences in dual affine connections naturally give rise to quantum interference and nonlocal correlations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a multi affine geometric framework to unify classical and quantum mechanical laws through the lens of information geometry. By combining the principle of stationary action with maximum entropy production, we show that divergences in dual affine connections naturally give rise to quantum interference and nonlocal correlations. These ideas of maximum entropy and stationary align with the framework of entropic dynamics, wherein time evolution emerges from information-theoretic principles. A key insight comes from Berry phases. the mismatch of multiple affine connections leads to a nontrivial holonomy or "area", explaining how Bell type inequalities can be violated up to the Tsirelson bound. Additionally, we interpret sharply peaked distributions as "pinning" or "sourcing" curvature in the information manifold, drawing an analogy to a membrane under uniform stress. In this view, entanglement and coherence emerge as geometric features, phases and rotations within an overarching multi affine structure. We conclude that phenomena such as wavefunction collapse and quantum steering can be viewed as constraints on the manifold's "laxity" or curvature, with far-reaching implications for understanding quantum behavior in a geometric-information setting.

Related papers

• 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)
• Many-body quantum geometry in time-dependent quantum systems with emergent quantum field theory instantaneously [13.437981636279718]
  We study many-body quantum geometric effects in time-dependent system with emergent quantum integrable field theory instantaneously. Our results unveil telltale quantum geometric signatures in time-dependent many-body systems, elucidating the intricate interplay between quantum geometry and dynamics.
  arXiv  Detail & Related papers  (2025-03-24T07:09:04Z)
• Quantum geometry embedded in unitarity of evolution: revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands [0.29127054707887967]
  We show how geometry emerges in quantum as an intrinsic consequence of unitary evolution.<n>We exemplify geometric observables, such as oscillation, dephasing, in spin and band scenarios.
  arXiv  Detail & Related papers  (2024-06-22T13:16:51Z)
• Observation of many-body dynamical localization [12.36065516066796]
  We present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.
  arXiv  Detail & Related papers  (2023-12-21T14:24:50Z)
• Lattice Holography on a Quantum Computer [10.205744392217532]
  We compute the ground state of a spin system on a $(2+1)$-dimensional hyperbolic lattice. We observe that with achievable resources for coming quantum devices, the correlation function demonstrates an approximate scale-invariant behavior.
  arXiv  Detail & Related papers  (2023-12-16T21:48:24Z)
• Topological Obstructions and How to Avoid Them [22.45861345237023]
  We show that local optima can arise due to singularities or an incorrect degree or winding number. We propose a new flow-based model that maps data points to multimodal distributions over geometric spaces.
  arXiv  Detail & Related papers  (2023-12-12T18:56:14Z)
• Geometric Phases in Open Quantum Systems: Analysis and Applications [0.0]
  This thesis explores the relation between decoherence and environmentally-induced dissipative effects. The first mention of such an object in the context of quantum mechanics goes back to the seminal work by Berry.
  arXiv  Detail & Related papers  (2023-07-07T20:39:24Z)
• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model [0.0]
  Modern geometry studies the interrelations between elements such as distance and curvature. We explore these structures in a physical system of $N$ interaction spin-$1/2$ under all-range Ising model.
  arXiv  Detail & Related papers  (2023-04-11T15:26:19Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Geometrical, topological and dynamical description of $\mathcal{N}$ interacting spin-$\mathtt{s}$ under long-range Ising model and their interplay with quantum entanglement [0.0]
  This work investigates the connections between integrable quantum systems with quantum phenomena exploitable in quantum information tasks. We find the relevant dynamics, identify the corresponding quantum phase space and derive the associated Fubini-Study metric. By narrowing the system to a two spin-$mathtts$ system, we explore the relevant entanglement from two different perspectives.
  arXiv  Detail & Related papers  (2022-10-29T11:53:14Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Quantum Polar Duality and the Symplectic Camel: a Geometric Approach to Quantization [0.0]
  We study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. We show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. We discuss the Hardy uncertainty principle and the less-known Donoho--Stark principle from the point of view of quantum polarity.
  arXiv  Detail & Related papers  (2020-09-22T16:55:28Z)

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.