A short note on relative entropy for a pair of intermediate subfactors

TL;DR

This paper explicitly computes the Pimsner-Popa probabilistic constant for pairs of intermediate subfactors and relates it to the Connes-Størmer relative entropy, generalizing previous results in subfactor theory.

Contribution

It provides a new explicit computation linking probabilistic constants and relative entropy for intermediate subfactors, extending classical results.

Findings

Explicit formulas for probabilistic constants

Relationship established between constants and relative entropy

Generalization of Pimsner-Popa's classical results

Abstract

Given a quadruple of finite index subfactors we explicitly compute the Pimsner-Popa probabilistic constant for the pair of intermediate subfactors and relate it with the corresponding Connes-St{\o}rmer relative entropy between them. This generalizes an old result of Pimsner and Popa.