By 1935, Schrödinger had already realised that the biggest gulf between quantum theory and our received classical preconceptions is that, when it comes to quantum systems, the whole is more than the sum of its parts. In classical physics, for instance, it is possible to totally describe the state of two systems – say, two objects sitting on a table – by first totally describing the state of the first system then totally describing the state of the second system. This is a fundamental property one expects of a classical, separable universe. However, as Schrödinger points out, there exist states predicted by quantum theory (and observed in the lab!) that do not obey this ‘obvious’ law about the physical world. Schrödinger called this new, totally non-classical phenomenon Verschränkung, which later became translated to the dominant scientific language as entanglement.

Quantum picturalism is all about studying the way parts compose to form a whole. In the good company of Schrödinger, we believe that the role of multiple interacting systems – especially non-separable systems – should take centre stage in the study of quantum theory.

We shall see in the next section that it is easy to say what it means for a process to be separable in terms of diagrams. Literally, it means that it can be broken up into pieces that are not connected to each other. On the other hand, enforcing non-separability requires us to refine our diagrammatic language. To this end, we introduce special states and effects called cups and caps, respectively. Intuitively, cups and caps act like pieces of wire that have been ‘bent sideways’.