Bumpified Haar Wavelets and Tsirelson's Bound: Some Mathematical Properties and Insights from Block Toeplitz Matrices

• URL: http://arxiv.org/abs/2410.13362v1
• Date: Thu, 17 Oct 2024 09:14:39 GMT
• Title: Bumpified Haar Wavelets and Tsirelson's Bound: Some Mathematical Properties and Insights from Block Toeplitz Matrices
• Authors: David Dudal, Ken Vandermeersch,
• Abstract summary: This paper investigates a recent construction using bumpified Haar wavelets to demonstrate explicit violations of the Bell-Clauser-Horne-Shimony-Holt inequality. Although a complete proof remains elusive, we present further compelling evidence to support it.
• Score: 0.0
• License:
• Abstract: This paper investigates a recent construction using bumpified Haar wavelets to demonstrate explicit violations of the Bell-Clauser-Horne-Shimony-Holt inequality within the vacuum state in quantum field theory. The construction was tested for massless spinor fields in $(1+1)$-dimensional Minkowski spacetime and is claimed to achieve violations arbitrarily close to an upper bound known as Tsirelson's bound. We show that this claim can be reduced to a mathematical conjecture involving the maximal eigenvalue of a sequence of symmetric matrices composed of integrals of Haar wavelet products. More precisely, the asymptotic eigenvalue of this sequence should approach $\pi$. We present a formal argument using a subclass of wavelets, allowing us to reach $3.11052$. Although a complete proof remains elusive, we present further compelling numerical evidence to support it.

Related papers

• Non-Hermitian expander obtained with Haar distributed unitaries [0.0]
  We consider a random quantum channel obtained by taking a selection of $d$ independent and Haar distributed $N$ dimensional unitaries. This shows that we have constructed a random quantum expander in terms of both singular values and eigenvalues.
  arXiv  Detail & Related papers  (2024-06-14T13:37:46Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory [0.0]
  We study the case of $3D$ $mathrmU(1)$ pure gauge theory, simulating the staggered case numerically in its dual formulation. We find evidence of a continuum limit with a spontaneously broken $bbZ$ single-site symmetry, in contrast to the ordinary theory. Moreover, the confining string fractionalizes into multiple strands which separate spatial regions in distinct ground states of the broken symmetry.
  arXiv  Detail & Related papers  (2023-09-29T10:08:21Z)
• Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets [0.0]
  We investigate the violation of the Bell-CHSH inequality in the vacuum state in the context of Quantum Field Theory. We test the method with massless spinor fields in $(1+1)$-dimensional Minkowski space-time. We briefly comment on the extra portal, compared to earlier works, this opens to scrutinize Bell-CHSH inequalities with generic, interacting Quantum Field Theories.
  arXiv  Detail & Related papers  (2023-07-10T14:53:39Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Topological Quantum Computation on Supersymmetric Spin Chains [0.0]
  Quantum gates built out of braid group elements form the building blocks of topological quantum computation. We show that the fusion spaces of anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains.
  arXiv  Detail & Related papers  (2022-09-08T13:52:10Z)
• Trimer states with $\mathbb{Z}_3$ topological order in Rydberg atom arrays [0.0]
  We study the quantum states obtained as equal-weight superpositions of all trimer coverings of a lattice. We show that these states can host $mathbbZ_3$ topological order or can be gapless liquids with $mathrmU(1) times mathrmU(1)$ local symmetry.
  arXiv  Detail & Related papers  (2022-05-20T18:04:58Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Existence of the first magic angle for the chiral model of bilayer graphene [77.34726150561087]
  Tarnopolsky-Kruchkov-Vishwanath (TKV) have proved that for inverse twist angles $alpha$ the effective Fermi velocity at the moir'e $K$ point vanishes. We give a proof that the Fermi velocity vanishes for at least one $alpha$ between $alpha approx.586$.
  arXiv  Detail & Related papers  (2021-04-13T20:37:00Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.