Year: 2025
Type: article
Abstract: We show a connection between the minimax and Bayes approaches in quantum decision theory in a general setting of normal states on a von Neumann algebra. In particular, the quantum minimax theorem is proven in a fairly general situation, and it is shown that every minimax strategy is Bayes for some a priori distribution on the set of states—a so-called least favourable prior . Minimax strategies with constant risk are investigated in some detail. It turns out that in dimension greater than two such a strategy can be Bayes for a non-uniform a priori distribution which, at the same time, is a least favourable prior.
Source: Quantum Information Processing
Author: Andrzej Łuczak
Institution: University of Łódź
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4414443863