Non-causal Page-Wootters circuits

Abstract

"The process matrix framework was invented to capture a phenomenon known as indefinite or quantum causal structure. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. We combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several observers, each with their own discrete quantum clock. This allows for implementing processes with indefinite casual order. The description via a history state with multiple clocks imposes constraints on the implementability of process matrices intros framework and on the perspectives of the observers. We describe how to to implement processes were the different definite causal orders are coherently controlled and explain why certain non-causal processes might not be implementable within this setting."