Bayesian inversion and the Tomita-Takesaki modular group

• URL: http://arxiv.org/abs/2112.03129v3
• Date: Mon, 23 Jan 2023 20:49:26 GMT
• Title: Bayesian inversion and the Tomita-Takesaki modular group
• Authors: Luca Giorgetti, Arthur J. Parzygnat, Alessio Ranallo, Benjamin P. Russo
• Abstract summary: We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita-Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional $C^*$-algebras.

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