Rethinking Causality in Quantum Mechanics

Abstract

Causality was always believed to be a well-defined fundamental concept in classical physics. However, the late efforts for a theory of quantum gravity have suggested that causal structures may not only be dynamical, as in general relativity, but also indefinite, the way a quantum observable has an indefinite value prior to its measurement. Based on this observation, it was proposed that some general probabilistic framework would be needed for the study of correlations between a number of events, without the assumption that a causal order between them exists. In this thesis we developed such a general probabilistic framework, independent of the theory that describes the events. We proposed a concept of causality, taking into account that there can be situations where the causal order may be dynamical; an event may affect the causal order of other events in its future. In that theory-independent framework, we formulated causality in terms of constraints that the correlations of the events should obey. In the case where the events are described by quantum mechanics, there is a different description of the correlations of the events, called a process matrix. In that theory-dependent framework, we found that causality in this case is expressed in terms of simple conditions on the process matrix. We observed the differences in which causality manifests at the level of the two frameworks. We worked further on the latter, to develop mathematical tools to probe situations incompatible with causal order. These tools allowed us to test computationally whether a given scenario is compatible with a causal order. Also, given an experimental realization of such a scenario, these tools provide us the operations that are required in the lab to prove incompatibility with causal order. Something which we plan to prove in our own labs. We also developed computational methods to obtain restrictions of causality in terms of inequalities, for a given scenario. We finished our study with a powerful and promising field of causality: causal discovery. Assuming that there is a well-defined and fixed causal order between a number of events, causal discovery aims at inferring the causal structure in which they are embedded by obtaining data from the events. We performed two complementary experiments that rule out a class of classical hidden variable causal models for Bell correlations. Finally, abandoning the idea that quantum events have a classical causal model, we use a quantum causal modeling framework to write the first quantum causal discovery algorithm.