Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

• URL: http://arxiv.org/abs/2501.03186v1
• Date: Mon, 06 Jan 2025 18:04:09 GMT
• Title: Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators
• Authors: M. S. Guimaraes, I. Roditi, S. P. Sorella, A. F. Vieira,
• Abstract summary: We construct a set of Hermitian dichotomic operators in relativistic Quantum Field Theory in Minkowski spacetime. Both Bell and Mermin inequalities are studied by means of a numerical setup.
• Score: 0.0
• License:
• Abstract: The use of the vacuum projector $|0 \rangle \langle 0| $ and of the unitary Weyl operators enables us to construct a set of Hermitian dichotomic operators in relativistic scalar Quantum Field Theory in Minkowski spacetime. Employing test functions supported in diamond regions, both Bell and Mermin inequalities are studied by means of a numerical setup. In addition to reporting expressive violations of both inequalities, the cluster property is also checked.

Related papers

• Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory [0.0]
  The Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter.
  arXiv  Detail & Related papers  (2024-06-28T16:24:24Z)
• Unruh-De Witt detectors, Bell-CHSH inequality and Tomita-Takesaki theory [0.0]
  The interaction between Unruh-De Witt spin $1/2$ detectors and a real scalar field is scrutinized. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom.
  arXiv  Detail & Related papers  (2024-01-06T22:01:33Z)
• Using Weyl operators to study Mermin's inequalities in Quantum Field Theory [0.0]
  We use the Tomita-Takesaki modular theory to compute the vacuum expectation value of the Mermin operator. We are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory.
  arXiv  Detail & Related papers  (2023-12-12T01:00:13Z)
• The Schmidt rank for the commuting operator framework [58.720142291102135]
  The Schmidt rank is a measure for the entanglement dimension of a pure bipartite state. We generalize the Schmidt rank to the commuting operator framework. We analyze bipartite states and compute the Schmidt rank in several examples.
  arXiv  Detail & Related papers  (2023-07-21T14:37:33Z)
• Moving mirror-field dynamics under intrinsic decoherence [77.34726150561087]
  We study the decaying dynamics in the mirror-field interaction by means of the intrinsic decoherence scheme. We show expectation values, correlations, and Husimi functions for the solutions obtained.
  arXiv  Detail & Related papers  (2023-05-06T03:41:45Z)
• Mermin's inequalities in Quantum Field Theory [0.46040036610482665]
  We introduce unitary operators which create, out of the Minkowski vacuum $| 0 rangle$, GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.
  arXiv  Detail & Related papers  (2023-03-21T20:56:58Z)
• Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory [0.0]
  We present an investigation of the $CHSH$ inequality within a relativistic quantum field theory model. A $CHSH$ type correlator is constructed and evaluated in the Fock vacuum by means of the canonical quantization. The model can be employed for the study of Bell's inequalities in the more physical case of gauge theories.
  arXiv  Detail & Related papers  (2022-10-28T19:15:57Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• 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.