From the 1 of 7 linked papers with an AI index.
3 citations · 4 across the 4 of their papers we have counts for
7 papers
Nonunital Operator Systems as Modules in Enriched Category Theory
Tim Netzer, Tobias Fritz
The paper shows that nonunital operator systems can be viewed as modules in an enriched categorical setting, establishing an equivalence with modules over matrix algebras enriched…
Monotone additive statistics on heavy-tailed convolution semigroups
Tobias Fritz, Xiaosheng Mu, Omer Tamuz
We study sub-semigroups of the semigroup of probability measures on and monotone additive statistics on them, by which we mean maps to the reals that are monotone with…
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…
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…
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…
Abstract Vergleichsstellensätze for preordered semifields and semirings II
Tobias Fritz
The present paper continues our foundational work on real algebra with preordered commutative semifields and semirings. We prove two abstract Vergleichsstellensätze for preordered…