https://doi.org/10.1140/epjc/s10052-025-14413-5
Regular Article - Theoretical Physics
Relative entropy of single-mode squeezed states in Quantum Field Theory
1
Instituto de Física-Departamento de Física Teórica, UERJ-Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, 20550-013, Rio de Janeiro, Brazil
2
CBPF-Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
3
Instituto de Física, Universidade Federal do Rio de Janeiro (UFRJ), 21.941-909, Rio de Janeiro, Brazil
Received:
22
April
2025
Accepted:
8
June
2025
Published online:
30
June
2025
Utilizing the Tomita–Takesaki modular theory, we derive a closed-form analytic expression for the Araki–Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field Theory within wedge regions of Minkowski spacetime. Similarly to the case of coherent states, this relative entropy is proportional to the smeared Pauli–Jordan distribution. Consequently, the Araki–Uhlmann entropy between a single-mode squeezed state and the vacuum satisfies all expected properties: it remains positive, increases with the size of the Minkowski region under consideration, and decreases as the mass parameter grows.
© The Author(s) 2025
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