302 citations · 2.7k across the 73 of their papers we have counts for
74 papers
Nonunital Operator Systems as Modules in Enriched Category Theory
Tim Netzer, Tobias Fritz
An operator system is similar to a module over a ring, with the role of scalar multiplication played by the action of completely positive maps. Using enriched category theory, we m…
The quantum instrument monad
Tobias Fritz
Monads are a ubiquitous structure in functional programming used for modelling computational effects. For example, the state monad models the effect of a computation interacting wi…
Why measurements are made of effects
Tobias Fritz
Both in quantum theory and in general probabilistic theories, measurements with outcomes are modelled as -tuples of \emph{effects} summing up to the unit effect. Why is this…
Absolute continuity, supports and idempotent splitting in categorical probability
Tobias Fritz, Tomáš Gonda, Antonio Lorenzin +2
Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like con…
Weakly Markov categories and weakly affine monads
Tobias Fritz, Fabio Gadducci, Paolo Perrone +1
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the…
Matrix majorization in large samples
Muhammad Usman Farooq, Tobias Fritz, Erkka Haapasalo +1
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into th…