Conference

Causal reasoning is vital for effective reasoning in many domains, from healthcare to economics. In medical diagnosis, for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. This is because causal relations, unlike correlations, allow one to reason about the consequences of possible treatments and to answer counterfactual queries. In this talk I will present two recent causal inference projects done with my collaborators deriving new algorithms to solve problems that arise when applying causal inference in the real world.

"Linear structural equation models relate random variables of interest via a linear equation system that features stochastic noise. The models are naturally represented by directed graphs whose edges indicate non-zero coefficients in the linear equations. In this talk I will report on progress on combinatorial conditions for parameter identifiability in models with latent (i.e., unobserved) variables. Identifiability holds if the coefficients associated with the edges of the graph can be uniquely recovered from the covariance matrix they define. Paper: https://doi.org/10.1214/22-AOS2221 or https://arxiv.org/abs/2201.04457"

There has been recent interest in extending the concept of contextuality to cases of disturbance or inconsistent connectedness. This talk will describe an approach using probabilistic causal models, which generalize the hidden-variables models of Bell and Kochen & Specker, following recent work by Cavalcanti. I first prove an equivalence between three conditions on an arbitrary measurement system: (1) existence of a model minimizing all causal influences of context upon measurement outcomes, (2) prohibition of a form of "hidden" causal influence, and (3) noncontextuality as defined in the Contextuality-by-Default (CbD) theory of Dzhafarov and Kujala. The no-hidden-influence principle thus confers a physical interpretation to CbD-contextuality, paralleling Bell's local causality and Kochen & Specker's classical embeddability. I then extend this analysis to other causal graph topologies, showing that different graphs yield different notions of contextuality, but only the one corresponding to CbD agrees with traditional contextuality when restricted to non-disturbing systems.

In a recent paper, Chaturvedi et al considered the interesting idea of routed Bell experiments. These are Bell experiments where Bob can measure his quantum particles at two distinct locations, one close to the source and another far away. This can be accomplished in the lab by using a switch that directs Bob's quantum particle either to the nearby measurement device or to the distant one, depending on a classical input chosen by Bob. Chaturvedi et al argue that there exists in such experiments a tradeoff between short-range and long-range correlations and that high-quality CHSH tests close to the source (which are achievable with current technology) lower the requirements for witnessing nonlocality faraway from the source, and in particular increase their tolerance to particle losses. We critically review their results and present a simple counterexample to it. We then introduce a class of hybrid quantum-classical models, which we refer to as "short-range quantum models". These models suitably capture the tradeoff between short-range and long-range correlations in routed Bell experiments. Using our definition, we explore new nonlocal tests in which high-quality short-range correlations lead to weakened conditions for long-range tests. Although we do find improvements, they are significantly smaller than those claimed by CVP.

"Many relevant tasks in Quantum Information processing can be expressed as polynomial optimization problems over states and operators. In the earlier talk by David, we saw that this is also the case for certain (quantum) causal compatibility and causal optimization problems. This talk will focus on several closely related semidefinite programming (SDP) hierarchies that have recently been shown to be complete for such polynomial optimization problems [arxiv:2110.14659, 2212.11299, 2301.12513]. We give a high-level overview of the techniques and mathematics that are needed for proving such statements. In particular, we will see a version of a Quantum De Finetti theorem, as well as a sketch of a constructive proof of convergence for the SDP hierarchies. Afterwards, these results are linked back to the causal compatibility problem to conclude that such SDP hierarchies are complete for a certain type of causal structures known as tree networks."