On the role of the unitary transformations in Bell inequalities

• URL: http://arxiv.org/abs/2412.03840v1
• Date: Thu, 05 Dec 2024 03:11:29 GMT
• Title: On the role of the unitary transformations in Bell inequalities
• Authors: D. O. R. Azevedo, F. M. Guedes, M. S. Guimaraes, I. Roditi, S. P. Sorella, A. F. Vieira,
• Abstract summary: We show how the violation of the Bell-CHSH inequality can be encoded into unitary transformations acting on a given reference set of Bell's observables. We show that using unitary transformations can significantly improve our previous numerical algorithm, leading to an increase in the size of the violation.
• Score: 0.0
• License:
• Abstract: The role of the unitary transformations in the Bell-CHSH inequality is highlighted, in both Quantum Mechanics and relativistic Quantum Field Theory. In the former case, we discuss, through a few examples, how the violation of the Bell-CHSH inequality can be encoded into unitary transformations acting on a given reference set of Bell's observables. In the latter case, the Bell-CHSH inequality for a real massive scalar field in the vacuum state is considered. After introducing suitable bounded Hermitian operators, we show that using unitary transformations can significantly improve our previous numerical algorithm, leading to an increase in the size of the violation.

Related papers

• Bell's inequality in relativistic Quantum Field Theory [0.0]
  A concise and self-contained introduction to the Bell inequality in relativistic Quantum Field Theory is presented. Taking the example of a real scalar massive field, the violation of the Bell inequality in the vacuum state and for causal complementary wedges is illustrated.
  arXiv  Detail & Related papers  (2024-10-24T19:05:05Z)
• Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality [0.0]
  The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum field is revisited by making use of the Hilbert space $cal H otimes cal H_AB$. The construction of Hermitian, field-dependent, dichotomic operators is devised as well as the Bell-CHSH inequality.
  arXiv  Detail & Related papers  (2024-07-19T19:14:00Z)
• Bell-CHSH inequality and unitary operators [0.0]
  Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The relevance of a particular class of unitary operators whose expectation values are real is pointed out.
  arXiv  Detail & Related papers  (2024-03-22T15:17:31Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• On the representations of Bell's operators in Quantum Mechanics [0.0]
  We show that when the dimension of the Hilbert space is greater than two, Bell's operators exhibit unitarily inequivalent representations. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.
  arXiv  Detail & Related papers  (2023-04-12T08:38:01Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Comments on the Bell-Clauser-Horne-Shimony-Holt inequality [0.0]
  In Quantum Mechanics the entangled spin singlet states are thought as the vacuum states of suitable Hamiltonians. The Bell-CHSH inequality turns out to be parametrized by the Unruh temperature.
  arXiv  Detail & Related papers  (2023-01-05T05:17:38Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.