Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916421204705280 |
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| author | Guimaraes, M. S. Roditi, I. Sorella, S. P. |
| author_facet | Guimaraes, M. S. Roditi, I. Sorella, S. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality Guimaraes, M. S. Roditi, I. Sorella, S. P. Quantum Physics High Energy Physics - Theory 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. |
| title | Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.14636 |