Quantum Causal Models

Abstract

Inferring cause and effect relations from observed correlations is a fundamental aspect of science. A causal modelling framework has been formulated to describe correlations among classical random variables arising from a causal structure and has found diverse applications in machine learning, economics, and clinical trials. However, experimental violations of Bell inequalities demonstrate the inadequacy of the classical framework in describing quantum correlations. Quantum causal models, involving quantum channels connecting quantum systems, provide an inherently quantum-mechanical description of causality that accurately reproduces quantum correlations. The framework has allowed the study of cyclic causal models, which are employed to describe exotic features of spacetime and physical feedback processes. For instance, within General Relativity, certain solutions allow a particle to return to its initial spacetime location, seemingly suggesting the theoretical possibility of time travel. Such scenarios give rise to various paradoxes, which can be studied by eliminating the cyclicity of the model through the implementation of the quantum teleportation protocol with post-selection. Finally, I will address the issue of how causality emerges from quantum correlations and demonstrate how this can be analysed by establishing a connection between tensor networks and causal models.