Glad you made it here! This book is about telling the story of quantum theory entirely in terms of pictures. Before we get into telling the story itself, it's worth saying a few words about how it came about. On the one hand, this is a very new story, in that it is closely tied to the past 10 years of research by us and our colleagues. On the other hand, one could say that it traces back some 80 years when the amazing John von Neumann denounced his own quantum formalism and embarked on a quest for something better. One could also say it began when Erwin Schrödinger addressed Albert Einstein's concerns about ‘spooky action at a distance’ by identifying the structure of composed systems (and in particular, their non-separability) as the beating heart of quantum theory.

From a complementary perspective, it traces back some 40 years when an undergraduate student named Roger Penrose noticed that pictures out-classed symbolic reasoning when working with the tensor calculus.

But 80 years ago the authors weren't around yet, at least not in human form, and 40 years ago there wasn't really that much of us either, so this preface will provide an egocentric take on the birth of this book. This also allows us to wholeheartedly acknowledge all of those without whom this book would never have existed (as well as some who nearly succeeded in killing it).

Things started out pretty badly for Bob, with a PhD in the 1990s on a then completely irrelevant topic of contextual ‘hidden variable representations’ of quantum theory – which recently have been diplomatically renamed to ontological models (Harrigan and Spekkens, 2010; Pusey et al., 2012). After a period of unemployment and a failed attempt to become a rock star, Bob ventured into the then even more irrelevant topic of von Neumann's quantum logic (Birkhoff and von Neumann, 1936) in the vicinity of the eccentric iconoclast Constantin Piron (1976).

It was there that category theory entered the picture, as well as serious considerations on the fundamental status of composition in quantum systems – something that went hand-in-hand with bringing quantum processes (rather than quantum states) to the forefront …