Related papers: Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality

Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality

URL: http://arxiv.org/abs/2407.14636v2
Date: Thu, 3 Oct 2024 10:25:05 GMT
Title: Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality
Authors: M. S. Guimaraes, I. Roditi, S. P. Sorella,
Abstract summary: 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum field is revisited by making use of the Hilbert space ${\cal H} \otimes {\cal H}_{AB}$, where ${\cal H}$ and ${\cal H}_{AB}$ stand, respectively, for the Hilbert space of the scalar field and of a generic bipartite quantum mechanical system. The construction of Hermitian, field-dependent, dichotomic operators is devised as well as the Bell-CHSH inequality. Working out the $AB$ part of the inequality, the resulting Bell-CHSH correlation function for the quantum field naturally emerges from unitary Weyl operators. Furthermore, introducing a Jaynes-Cummings type Hamiltonian accounting for the interaction between the scalar field and a pair of qubits, the quantum corrections to the Bell-CHSH inequality in the vacuum state of the scalar field are evaluated till the second order in perturbation theory.

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)
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)
Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling [44.99833362998488]
We discuss entanglement and violation of Bell-type inequalities for a system of two $Z$ bosons produced in Higgs decays. We find that a $ZZ$ state is entangled and violates the inequality for all values of the pair (anomalous) coupling constant.
arXiv Detail & Related papers (2023-07-25T13:44:31Z)
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)
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)
Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
arXiv Detail & Related papers (2022-09-12T08:21:12Z)
Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z)
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)
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.