  We provide a new way to bound the security of quantum key distribution using
only two high-level, diagrammatic features of quantum processes: the
compositional behavior of complementary measurements and the essential
uniqueness of purification. We begin by demonstrating a proof in the simplest
case, where the eavesdropper doesn't noticeably disturb the channel at all and
has no quantum memory. We then show how this approach extends straightforwardly
to account for an eavesdropper with quantum memory and the presence of noise.
