  Within the Geometry of Interaction (GoI) paradigm, we present a setting that
enables qualitative differences between classical and quantum processes to be
explored. The key construction is the physical interpretation/realization of
the traced monoidal categories of finite-dimensional vector spaces with tensor
product as monoidal structure and of finite sets and relations with Cartesian
product as monoidal structure, both of them providing a so-called wave-style
GoI. The developments in this paper reveal that envisioning state update due to
quantum measurement as a process provides a powerful tool for developing
high-level approaches to quantum information processing.
