TensorTalk: Jonathan Barrett

Speaker: Jonathan Barrett (QIP'20 Video)

Title: Quantum Causal Models

Abstract:
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. Efforts have been devoted towards generalization of the classical framework to the quantum case, with the aim of providing a framework in which cause-effect relations between quantum systems, and their connection with empirically observed data, can be rigorously analyzed. Building on the results of Allen et al., Phys. Rev. X 7, 031021 (2017), we present a fully-fledged framework of quantum causal models.
The approach situates causal relations in unitary transformations, in analogy with an approach to classical causal models that assumes underlying determinism and situates causal relations in functional dependences between variables. We show that for any quantum causal model, there exists a corresponding unitary circuit, with appropriate causal structure, such that the quantum causal model is returned when marginalising over latent systems, and vice versa. We introduce an intrinsically quantum notion that plays a role analogous to the conditional independence of classical variables, and (generalizing a central theorem of the classical framework) show that d-separation is sound and complete in the quantum case. We present generalizations of the three rules of the classical `do-calculus', in each case relating a property of the causal structure to a formal property of the quantum process, and to an operational statement concerning the outcomes of interventions. In addition to the results concerning quantum causal models, we introduce and derive similar results for `classical split-node causal models', which are more closely analogous to quantum causal models than the classical causal models that are usually studied.

Here is a link to the QIP talk: https://www.koushare.com/video/videodetail/4185

It is based on this paper: https://arxiv.org/abs/1906.10726?

By Jonathan Barrett, Robin Lorenz, Ognyan Oreshkov.