Categorical Semantics for Time Travel

Nicola Pinzani(University of Oxford), Stefano Gogioso (University of Oxford), Bob Coecke (University of Oxford)

We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide computational speedups. Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms.

We show that the two leading models for quantum theory with closed timelike curves—namely the P-CTC model of Lloyd et al. and the D-CTC model of Deutsch—are captured by our framework, and in doing so we provide the first compositional description of the D-CTC model. Our description of the D-CTC model results in a process theory which respects the constraints of relativistic causality: this is in direct contrast to the P-CTC model, where CTCs are implemented by a trace and allow post-selection to be performed deterministically.

(This work has been accepted for presentation at LICS2019 and will be submitted as a 3-page extended abstract)