Investigating the Araki-Uhlmann relative entropy between two coherent states in relativistic Quantum Field Theory

Abstract

A numerical setup for investigating the Araki-Uhlmann relative entropy between two coherent states is presented for a scalar massive Quantum Field Theory in ($1+1$)-dimensional Minkowski spacetime. These states are constructed using smeared Weyl operators compactly supported in two diamond regions belonging to the right Rindler wedge. Using this setup, we verified the known properties of the relative entropy, namely: positivity, increase with the size of the spacetime regions considered, decrease with the increase of the mass parameter. A linear increase with respect to the spatial distance between the two diamond regions is also observed.

10 pages, 4 figures; typos corrected

References in corpus (5)

• Entropy of Coherent Excitations
• Entropy for spherically symmetric, dynamical black holes from the relative entropy between coherent states of a scalar quantum field
• Relative Entropy of Fermion Excitation States on the CAR Algebra
• Bell's inequality in relativistic Quantum Field Theory
• Relative entropy of an interval for a massless boson at finite temperature