Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model

• URL: http://arxiv.org/abs/2304.05278v3
• Date: Fri, 30 Aug 2024 20:43:28 GMT
• Title: Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model
• Authors: Jamal Elfakir, Brahim Amghar, Abdallah Slaoui, Mohammed Daoud,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: With the growth of geometric science, including the methods of exploring the world of information by means of modern geometry, there has always been a mysterious and fascinating ambiguous link between geometric, topological and dynamical characteristics with quantum entanglement. Since geometry studies the interrelations between elements such as distance and curvature, it provides the information sciences with powerful structures that yield practically useful and understandable descriptions of integrable quantum systems. We explore here these structures in a physical system of $N$ interaction spin-$1/2$ under all-range Ising model. By performing the system dynamics, we determine the Fubini-Study metric defining the relevant quantum state space. Applying Gaussian curvature within the scope of the Gauss-Bonnet theorem, we proved that the dynamics happens on a closed two-dimensional manifold having both a dumbbell-shape structure and a spherical topology. The geometric and topological phases appearing during the system evolution processes are sufficiently discussed. Subsequently, we resolve the quantum brachistochrone problem by achieving the time-optimal evolution. By restricting the whole system to a two spin-$1/2$ system, we investigate the relevant entanglement from two viewpoints; The first is of geometric nature and explores how the entanglement level affects derived geometric structures such as the Fubini-Study metric, the Gaussian curvature, and the geometric phase. The second is of dynamic nature and addresses the entanglement effect on the evolution speed and the related Fubini-Study distance. Further, depending on the degree of entanglement, we resolve the quantum brachistochrone problem.

Related papers

• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• 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)
• 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)
• Measuring quantum geometric tensor of non-Abelian system in superconducting circuits [21.82634956452952]
  We use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. We reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.
  arXiv  Detail & Related papers  (2022-09-26T01:08:39Z)
• Geometric phase and its applications: topological phases, quantum walks and non-inertial quantum systems [0.0]
  We have proposed a fresh perspective of geodesics and null phase curves, which are key ingredients in understanding the geometric phase. We have also looked at a number of applications of geometric phases in topological phases, quantum walks, and non-inertial quantum systems.
  arXiv  Detail & Related papers  (2022-09-11T08:01:17Z)
• Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
  A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Programmable Interactions and Emergent Geometry in an Atomic Array [0.0]
  Nonlocal interactions govern the flow of information and the formation of correlations in quantum systems. We report on the realization of programmable nonlocal interactions in an array of atomic ensembles within an optical cavity. Our work opens broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization algorithms, and engineering new entangled resource states for sensing and computation.
  arXiv  Detail & Related papers  (2021-06-08T03:00:49Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.