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 …

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 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 …

Coassociativity of∆ follows from associativity of the product in G. To see that the cancellation
property holds, note that (A⊗ 1)∆(A) is the unital∗-subalgebra of C (G× G) spanned by all …

Interaction trees (ITrees) are a general-purpose data structure for representing the behaviors
of recursive programs that interact with their environments. A coinductive variant of “free …

We propose the design of a programming language for quantum computing. Traditionally,
quantum algorithms are frequently expressed at the hardware level, for instance in terms of …

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it
became clear that underlying these diagrams is a powerful analogy between quantum …

Repetitive and ambiguous visual structures in general pose a severe problem in many
computer vision applications. Identification of incorrect geometric relations between images …

Our aim is to revisit the mathematical foundations of quantum mechanics from a novel point
of view. The standard axiomatic presentation of quantum mechanics in terms of Hilbert …

The categorical notion of monad, used by Moggi to structure denotational descriptions, has
proved to be a powerful tool for structuring combinator libraries. Moreover, the monadic …