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String diagrams for C*-algebras and Bayesian inversion
Miércoles 03 Marzo 2021, 01:00pm
Accesos : 191
Contacto Carlos Segovia

Seminario de Categorías

Expositor: Arthur Parzygnat (IHÉS).

Resumen: The foundations of probability, statistics, and information theory are slowly undergoing a potentially dramatic change of perspective through the language of category theory via string diagrams [3]. This point of view has been abstracted to finite-dimensional C*-algebras via a stochastic variant of the Gelfand—Naimark theorem and quantum Markov categories. Through this abstraction, one can immediately analyze concepts such as Bayesian inversion in non-classical settings, which in fact has recently been done in finite dimensions [2]. What can be said for more general (possibly infinite dimensional) C*-algebras? In this talk, I will review some background on Markov categories, provide some motivation for their study, introduce our main quantum example, and then I'll provide a small refresher on C*-tensor products. Then, I'll explain why all C*-algebras do not form a quantum Markov category, and I will provide some suggestions for an alternative framework [1].

Main reference:

[1] (especially Remark 3.12 and Question 3.25).

Additional references of potential interest:

[2] (on Bayesian inversion in quantum mechanics)

[3] (on classical Markov categories) 

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