Indefinite causal order and the operational definition of events in perspective

The field of indefinite causal order born as a tentative to generalize quantum mechanics to a theory with no predefined causal structure, aiming to find a consistent framework for a quantum gravity theory. One key feature of this formulation is the understanding of what is an event, where from an operational view, an event is defined by operations applied on a quantum system inside a closed laboratory.

In contrast, in general relativity, and even in few theories of quantum gravity, an event is defined as a point on a manifold. These two definitions oppose each other in specific examples, raising discussions on what can be considered a genuine task with indefinite causal order, and what should be considered just a simulation.

In this talk, I will discuss not just these two definitions of event, but a few others that appear in the literature. This discussion will be based on the review of some different realizations and proposals of the most famous task with indefinite causal order: the quantum switch. Firstly, I will discuss the optical experiments of quantum switch, and also one proposal of a gravitational quantum switch. Secondly, I will show intermediate situations, which are contributions of mine, in which the agents used to perform a quantum switch are in an entangled state of different accelerations, or lie on a curved spacetime in an entangled state of different heights. Regardless of the definition of event, we show that the latter case can be used as a test on the interplay of quantum physics and general relativity using the gravity of Earth, and this proposal is expected to be realized with current technology. Finally, I will summarize all different definitions of event and how each one is related to the interpretation of each scenario of quantum switch.