Physical Traces Quantum vs. Classical Information Processing

AbstractWithin 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