# Categorical Probabilistic Theories

@article{Gogioso2017CategoricalPT, title={Categorical Probabilistic Theories}, author={Stefano Gogioso and Carlo Maria Scandolo}, journal={arXiv: Quantum Physics}, year={2017} }

We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM and OPTs have found successful application to a number of areas in quantum foundations and information theory: they present many similarities, both in spirit and in formalism, but they remain separated by a number of subtle yet important differences. We attempt…

## 35 Citations

### Categorical Operational Physics

- MathematicsArXiv
- 2019

This thesis gives a recipe for recovering a class of generalised quantum theories, before instantiating it with operational principles inspired by an earlier reconstruction due to CDP, and reconstructs finite-dimensional quantum theory itself.

### A Shortcut from Categorical Quantum Theory to Convex Operational Theories

- Mathematics
- 2018

This paper charts a very direct path between the categorical approach to quantum mechanics, due to Abramsky and Coecke, and the older convex-operational approach based on ordered vector spaces…

### A computer scientist’s reconstruction of quantum theory

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- 2022

The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order…

### Discrimination of symmetric states in operational probabilistic theory

- Mathematics
- 2020

A state discrimination problem in an operational probabilistic theory (OPT) is investigated in diagrammatic terms. It is well-known that, in the case of quantum theory, if a state set has a certain…

### Fantastic Quantum Theories and Where to Find Them

- Mathematics
- 2017

We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive…

### Compositional resource theories of coherence

- Computer ScienceQuantum
- 2020

This work shows that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory, and opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.

### Categorical quantum dynamics

- Computer Science, Mathematics
- 2016

It is argued that strong complementarity is a truly powerful and versatile building block for quantum theory and its applications, and one that should draw a lot more attention in the future.

### Classicality without local discriminability: Decoupling entanglement and complementarity

- Computer SciencePhysical Review A
- 2020

It is demonstrated that the presence of entanglement is independent of the existence of incompatible measurements, and on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, a no-go conjecture is formulated for theexistence of a local-realistic ontological model.

### Functorial Evolution of Quantum Fields

- Computer ScienceFrontiers in Physics
- 2021

A compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes and introduces notions of symmetry and cellular automata, which are shown to subsume existing definitions of Quantum Cellular Automata from previous literature.

### A no-go theorem for theories that decohere to quantum mechanics

- Philosophy, PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

This work asks whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism and proves that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification.

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