Why did it take us 50 years since the birth of the quantum mechanical formalism to discover
that unknown quantum states cannot be cloned? Yet, the proof of the 'no-cloning theorem'is …

Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio
is not an integer! But this can happen for generalizations of vector spaces--objects of a …

Categories enriched with tensor products, here called tensor categories, but also called
monoidal categories, have been studied and used extensively in the literature [ML1, EK …

We develop Markov categories as a framework for synthetic probability and statistics,
following work of Golubtsov as well as Cho and Jacobs. This means that we treat the …

This article is intended as a reference guide to various notions of monoidal categories and
their associated string diagrams. It is hoped that this will be useful not just to …

Monoidal category theory serves as a powerful framework for describing logical aspects of
quantum theory, giving an abstract language for parallel and sequential composition, and a …

This paper has two tightly intertwined aims:(i) to introduce an intuitive and universal
graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies …

Many fields of science investigate states and processes as resources. Chemistry,
thermodynamics, Shannon's theory of communication channels, and the theory of quantum …

We investigate general probabilistic theories in which every mixed state has a purification,
unique up to reversible channels on the purifying system. We show that the purification …

We formulate rational conformal field theory in terms of a symmetric special Frobenius
algebra A and its representations. A is an algebra in the modular tensor category of Moore …