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Oxford Quantum Talks Archive

Causal categories: a backbone for a quantum-relativistic universe of interacting processes

Ray Lal, University of Oxford
Quantum Physics and Logic 2010, May 2010, University of Oxford

We encode causal space-time structure within categorical process structure, by restricting the tensor to space-like separated entities, i.e.~between which there is no causal flow of information. In such a causal category, a privileged set of morphisms captures the idea of an event horizon. This structure enables us to derive statements independent of specific models and detailed descriptions of processes, for example, that for a teleportation-like configuration from which the classical channel is removed, information flow from Alice to Bob cannot occur. We show that causal categories with compact structures or a dagger collapse, and define a process projector which recovers the full power of categorical quantum mechanics.

[video] [streaming video]