  Dirac notation is the most common way to describe quantum states and
operations on states. It is very convenient and allows for quick visual
distinction between vectors, scalars and operators. For quantum processes that
involve interactions of multiple systems an even better visualisation has been
proposed by Coecke and Kissinger, in the form of a diagrammatic formalism
[CK2017]. Their notation expresses formulas in the form of diagrams, somewhat
similar to Feynman diagrams, and is more general than the circuit notation for
quantum computing.
  This document consists of two parts. (1) We give a brief summary of the
diagrammatic notation of quantum processes, tailored to readers who already
know quantum physics and are not interested in general process theory. For this
audience our summary is less daunting than the encyclopaedic book by Coecke and
Kissinger [CK2017], and on the other hand more accessible than the
ultra-compact introduction of [KTW2017]. We deviate a somewhat from
[CK2017,KTW2017] in that we do not assume basis states to equal their own
complex conjugate; this means that we do not use symmetric notation for basis
states, and it leads us to explicitly show arrows on wires where they are
usually omitted.
  (2) We extend the work of Kissinger, Tull and Westerbaan [KTW2017] which
gives a diagrammatic security proof for BB84 and 6-state Quantum Key
Distribution. Their proof is based on a sequence of diagrammatic manipulations
that works when the bases used in the protocol are mutually unbiased. We extend
this result to 8-state encoding, which has been proposed as a tool in quantum
key recycling protocols [SdV2017,LS2018], and which does not have mutually
unbiased bases.
