DeepAI AI Chat
Log In Sign Up

Effectus of Quantum Probability on Relational Structures

05/01/2020
by   Octavio Zapata, et al.
0

The notion of effectus from categorical logic is relevant in the emerging field of categorical probability theory. In some cases, stochastic maps are represented by maps in the Kleisli category of some probability monad. Quantum homomorphisms from combinatorics and quantum information theory are the Kleisli maps of certain sort of quantum monad. We show that the Kleisli category of this quantum monad is an effectus. This gives rise to notions of quantum probabilistic reasoning as predicates, validity, conditioning, and channels.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/29/2019

Universal Properties in Quantum Theory

We argue that notions in quantum theory should have universal properties...
04/21/2019

Quantum channels as a categorical completion

We propose a categorical foundation for the connection between pure and ...
02/01/2019

Categorical Operational Physics

Many insights into the quantum world can be found by studying it from am...
12/13/2021

Composable constraints

We introduce a notion of compatibility between constraint encoding and c...
12/30/2021

Quantum Operads

The most standard description of symmetries of a mathematical structure ...
11/07/2018

Hypernormalisation, linear exponential monads and the Giry tricocycloid

We provide new categorical perspectives on Jacobs' notion of hypernormal...
02/02/2021

Conditional distributions for quantum systems

Conditional distributions, as defined by the Markov category framework, ...