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 …

The ZX-calculus is a graphical language for reasoning about quantum computation that has
recently seen an increased usage in a variety of areas such as quantum circuit optimisation …

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 …

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 …

We formalise the constructive content of an essential feature of quantum mechanics: the
interaction of complementary quantum observables, and information flow mediated by them …

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 …

Categorical quantum mechanics places finite-dimensional quantum theory in the context of
compact closed categories, with an emphasis on diagrammatic reasoning. In this framework …

In this chapter we survey some particular topics in category theory in a somewhat
unconventional manner. Our main focus will be on monoidal categories, mostly symmetric …

We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently
characterised as a commutative†-Frobenius monoid in the category FdHilb, which has finite …