ABSTRACT
Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant algebraic approach by listing exactly all the equality constraints on the observed variables. However, this algebraically motivated causal model comprises distributions outside Bayesian networks, and its physical interpretation remains vague. In this talk, I will introduce our recent results on this topic, where we inspect the nested Markov model through the lens of generalized probabilistic theory (GPT). We prove that all the equality constraints defining the nested Markov model are valid theory-independently. At the same time, not every distribution within the nested Markov model is physically implementable. To interpret the origin of such a gap, we study three causal models standing between the nested Markov model and the set of all distributions admitting some GPT realization, each of which manifests new types of GPT-inviolable constraints. We hope our results will enlighten further explorations to unify algebraic and physical perspectives of causality.
BIOGRAPHY
Dr Xingjian Zhang is a Visiting Research Fellow at the National University of Singapore, hosted by Prof Hoi-Kwong Lo, and will soon join the University of Technology Sydney as a Chancellor’s Research Fellow. He received his PhD from Tsinghua University and completed his postdoctoral research at the University of Hong Kong. Dr Zhang’s research focuses on the theory and applications of quantum nonlocality. His work has been published in journals including Nature, Nature Communications, Physical Review Letters, and PNAS, and he has presented at conferences including TQC and AQIS. Leveraging his expertise in device-independent quantum cryptography, Dr Zhang also served on the ITU standardisation focus group for “Quantum information technology for networks” (QIT4N-I-018).
Date & Time
Venue
Chair