Colour degree matrix problems, also known as edge-disjoint realisation and edge packing problems, have connections for example to discrete tomography. Necessary and sufficient conditions are known for a demand matrix to be the colour degree matrix of an edgecoloured forest. We will give necessary and sufficient conditions for a demand matrix to be realisable by a graph with at most one cycle, and a polynomial time algorithm to check these conditions.

Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus [11]. This diagrammatic notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis [18] it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard's quantum key distribution protocol, BB84. Two of the protocols in [18], namely superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W -state, will be presented in this paper.