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arXiv:2303.12195 · Physics Letters B

Mermin's inequalities in Quantum Field Theory

Philipe De Fabritiis, I. Roditi, Silvio Paolo sorella

Published Sep 25, 2023• 6 citations
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Abstract

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.

DOI
10.1016/j.physletb.2023.138198

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A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.
Mermin’s inequalities are investigated in a quantum field theory framework by using von Neumann algebras built with Weyl operators. We devise a general construction based on the Tomita-Takesaki modular theory and use it to compute the vacuum expectation value of the Mermin operator, analyzing the parameter space and explicitly exhibiting a violation of Mermin’s inequalities. Therefore, relying on the power of modular operators, we are able to demonstrate that Mermin’s inequalities are violated when examined within the vacuum state of a scalar field theory. Published by the American Physical Society 2024
In this paper, it is proved that the maximal violation of Mermin's inequalities of nnn qubits occurs only for GHZ's states and the states obtained from them by local unitary transformations. The key point of our argument involved here is by using the certain algebraic properties that Pauli's matrices satisfy, which is based on the determination of local spin observables of the associated Bell-Mermin operators.
Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The ensuing modifications affecting both classical and quantum bounds are elucidated. The relevance of a particular class of unitary operators whose expectation values are real is pointed out. For these operators, the classical and quantum bounds remain unaltered, being given, respectively, by 2 and 2 2 . As examples, we discuss the explicit realization of phase space Bell-CHSH inequality violation and the Weyl unitary operators for a real scalar field in relativistic Quantum Field Theory.
Abstract Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic quantum field theory. The case of the scalar field in 1+11+11+1 1 + 1 Minkowski space-time is scrutinized by relying on the Tomita–Takesaki modular theory. The example of the bounded Hermitian operator sign(φ(f))sign(\varphi (f))sign(φ(f)) s i g n ( φ ( f ) ) , where φ(f)\varphi (f)φ(f) φ ( f ) stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.