Petz-Rényi relative entropy in QFT from modular theory

Abstract

We consider the generalization of the Araki-Uhlmann formula for relative entropy to Petz-Rényi relative entropy. We compute this entropy for a free scalar field in the Minkowski wedge between the vacuum and a coherent state, as well as for the free chiral current in a thermal state. In contrast to the relative entropy which in these cases only depends on the sympletic form and thus reduces to the classical entropy of a wave packet, the Petz-Rényi relative entropy also depends on the symmetric part of the two-point function and is thus genuinely quantum. We also consider the relation with standard subspaces, where we define the Rényi entropy of a vector and show that it admits an upper bound given by the entropy of the vector.

22 pages, matches published version

References in corpus (5)

• The entropic $g$-theorem in general spacetime dimension
• Entropy of Coherent Excitations
• Relative Entropy of Fermion Excitation States on the CAR Algebra
• Relative Entropy in de Sitter is a Noether Charge
• Entropy-area law and temperature of de Sitter horizons from modular theory

Cited by in corpus (1)

• Relative entropy of single-mode squeezed states in Quantum Field Theory