DeepAI AI Chat
Log In Sign Up

Universal Properties in Quantum Theory

by   Mathieu Huot, et al.

We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel. Physically, quantum channels are derived from pure quantum theory by allowing discarding. We phrase this in category theoretic terms by showing that the category of CPTP maps is the universal monoidal category with a terminal unit that has a functor from the category of isometries. In other words, the CPTP maps are the affine reflection of the isometries.


page 1

page 2

page 3

page 4


Universal Properties of Partial Quantum Maps

We provide a universal construction of the category of finite-dimensiona...

Effectus of Quantum Probability on Relational Structures

The notion of effectus from categorical logic is relevant in the emergin...

The Category of von Neumann Algebras

In this dissertation we study the category of completely positive normal...

Axioms for retrodiction: achieving time-reversal symmetry with a prior

We propose a category-theoretic definition of retrodiction and use it to...

Physical Implementability of Quantum Maps and Its Application in Error Mitigation

Completely positive and trace-preserving maps characterize physically im...

Quantum channels as a categorical completion

We propose a categorical foundation for the connection between pure and ...

Coend Optics for Quantum Combs

We compare two possible ways of defining a category of 1-combs, the firs...