36 citations · 80 across the 8 of their papers we have counts for
9 papers
Interpreting Lambda Calculus in Domain-Valued Random Variables
Robert Furber, Radu Mardare, Prakash Panangaden +1
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction r…
Scott Continuity in Generalized Probabilistic Theories
Robert Furber
Scott continuity is a concept from domain theory that had an unexpected previous life in the theory of von Neumann algebras. Scott-continuous states are known as normal states, and…
Probabilistic logics based on Riesz spaces
Robert Furber, Radu Mardare, Matteo Mio
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of…
Categorical Equivalences from State-Effect Adjunctions
Robert Furber
From every pair of adjoint functors it is possible to produce a (possibly trivial) equivalence of categories by restricting to the subcategories where the unit and counit are isomo…
Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras
Mathys Rennela, Sam Staton, Robert Furber
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras…
Unordered Tuples in Quantum Computation
Robert Furber, Bas Westerbaan
It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pai…
Towards a Categorical Account of Conditional Probability
Robert Furber, Bart Jacobs
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certa…
From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality
Robert W. J. Furber, Bart P. F. Jacobs
C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (co…
The Expectation Monad in Quantum Foundations
Bart Jacobs, Jorik Mandemaker
The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the di…