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 …

A reconstruction of quantum theory refers to both a mathematical and a conceptual
paradigm that allows one to derive the usual formulation of quantum theory from a set of …

In this paper, we develop a graphical calculus to rewrite photonic circuits involving light-
matter interactions and non-linear optical effects. We introduce the infinite ZW calculus, a …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

We introduce a construction that turns a category of pure state spaces and operators into a
category of observable algebras and superoperators. For example, it turns the category of …

Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them
suitable to express resource-sensitive systems, in which variables cannot be copied or …

Strong monads are important for several applications, in particular, in the denotational
semantics of effectful languages, where strength is needed to sequence computations that …

We present a new model of computation, described in terms of monoidal categories. It
conforms to the Church–Turing Thesis, and captures the same computable functions as the …

We introduce a novel compositional description of Feynman diagrams, with well-defined
categorical semantics as morphisms in a dagger-compact category. Our chosen setting is …

New scientific paradigms typically consist of an expansion of the conceptual language with
which we describe the world. Over the past decade, theoretical physics and quantum …