北京雁栖湖应用数学研究院

程嵩 , 丁大威 , 刘锦鹏 , 刘正伟 , 刘子文

张行健

2024年11月22日 16:00 至 17:30

Shuangqing-B627

Zoom 230 432 7880 (BIMSA)

Understanding causal relationships is an everlasting theme of scientific research. To interpret correlations between observed variables, a natural thought suggests causal explanations. In classical causal theories, all the variables, including both observed and latent ones, are modelled as random variables. However, as shown by the renowned Bell’s theorem, the classical formulation is incomplete when the latent variables enjoy a quantum nature. In this talk, I will present a new causal model formulated solely from the concept of independence. At a high level, we treat every causal structure as a low-dimensional projection from a high-dimensional Bell-type structure, where valid correlations among observed variables are projected from correlations in the Bell-type structure subjected to the independence conditions. We prove this formulation comprises all the predictions in generalized probabilistic theories. From a mathematical perspective, it reproduces the nested Markov model, an algebraically complete causal model defined by all the equality constraints within a causal structure. Moreover, we show inequality constraints may emerge from the projection of the equality constraints of independence. Nevertheless, we also present causal structures where “physical operations” pose stringently additional inequality constraints. Considering the undebatable role of independence in physics and algebra, we suggest the new model supersets any physically motivated causal theory. If time allows, I will also discuss applications of the new model in causal inference and the discovery of non-classical causal structures.

http://arxiv.org/abs/2411.11614

Xingjian Zhang is now a postdoctoral fellow at the Department of Computer Science, University of Hong Kong. He graduated from the Institute for Interdisciplinary Information Sciences (IIIS) at Tsinghua University in 2023 and obtained a PhD degree in physics. Xingjian Zhang is mainly dedicated to the theoretical study of quantum foundation and quantum communication. Thus far, Xingjian Zhang has published research papers in top journals, including PRL, PNAS, PRX Quantum, and Quantum, and has presented contributed talks at top conferences of quantum information, including TQC and AQIS. Based on his experiences, Xingjian Zhang participated in the ITU Standardization of ‘Quantum information technology for networks’ (QIT4N-I-018, focus group) and served as a reviewer for journals and conferences, including Nat. Commun., Phys. Rev. Lett., Sci. Adv., IEEE Trans. Inf. Theor., SODA, QIP, and TQC.