State retrieval beyond Bayes' retrodiction


Surace, J. (2023). State retrieval beyond Bayes' retrodiction. Perimeter Institute. https://pirsa.org/23010098


Surace, Jacopo. State retrieval beyond Bayes' retrodiction. Perimeter Institute, Jan. 12, 2023, https://pirsa.org/23010098


          @misc{ pirsa_PIRSA:23010098,
            doi = {10.48660/23010098},
            url = {https://pirsa.org/23010098},
            author = {Surace, Jacopo},
            keywords = {Quantum Foundations},
            language = {en},
            title = {State retrieval beyond Bayes{\textquoteright} retrodiction},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jan},
            note = {PIRSA:23010098 see, \url{https://pirsa.org}}

Jacopo Surace Perimeter Institute for Theoretical Physics


In the context of irreversible dynamics, the meaning of the reverse of a physical evolution can be quite ambiguous. It is a standard choice to define the reverse process using Bayes' theorem, but, in general, this is not optimal with respect to the relative entropy of recovery. In this work we explore whether it is possible to characterise an optimal reverse map building from the concept of state retrieval maps. In doing so, we propose a set of  principles that state retrieval maps should satisfy. We find out that the Bayes inspired reverse is just one case in a whole class of possible choices, which can be optimised to give a map retrieving the initial state more precisely than the Bayes rule. Our analysis has the advantage of naturally extending to the quantum regime. In fact, we find a class of reverse transformations containing the Petz recovery map as a particular case, corroborating its interpretation as a quantum analogue of the Bayes retrieval.

Finally, we present numerical evidence showing that by adding a single extra axiom one can isolate for classical dynamics the usual reverse process derived from Bayes' theorem.

Zoom link:  https://pitp.zoom.us/j/93589286500?pwd=dkZuRzR0SlhVd1lPdGNOZWFYQWtRZz09