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arXiv · 2411.09696

Petz-Rényi relative entropy in QFT from modular theory

Markus B. Fröb·Leonardo Sangaletti
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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.

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Markus B. Fröb, Leonardo Sangaletti. 2025-03-17. Petz-Rényi relative entropy in QFT from modular theory. https://doi.org/10.1007/s11005-025-01923-2

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