Quantum Entropic Causal Inference
Abstract
The goal of this program is to build the foundational theoretical framework for quantum causality that can be scaled up to N-qubits. We put forth a quantum entropic approach to causal inference that can discern the difference between causation and correlation. We propose to develop an entropic approach that will capture both the classical and quantum graphical causal inference in a unified framework. Our approach rests on comparing entropic measures from the data to quantify the influence of hidden variables in all directions (i.e. causal and non-causal). Classically, it has been proposed and tested that minimization of the information Entropy of exogenous variables identifies the causal direction. We will provide the first generalization of this result to the quantum domain by exploiting entanglement entropy of hidden variables. A major challenge is to develop computationally tractable greedy algorithms to identify this entropic measure solely from multi-variate joint distributions of input data. To this end, we provide preliminary results on classical cause-effect repositories to show that extracting entropy of exogenous latent variables is indeed possible. There exists no such quantum cause-effect repository that can guide the research community in their efforts. Therefore, we will leverage our previous work on time-dependent simulations of interacting noisy N-qubits to generate quantum cause-effect measurement pairs beyond the two qubit regime. We believe such a quantum repository is not only an important temporary solution till highly controlled experimental data becomes widely available but it can also have long-term impact on development of new error correcting codes, next generation Bell’s inequalities and quantum causal inference techniques. Finally, we put forth approaches to understand causal graphs (beyond two nodes) in the quantum domain using information theoretic inequalities. This work exploits generalization of Bell’s inequalities to large number of observers with increased measurement settings. Thus our program brings together ideas from time-dependent N-qubit simulation, classical+quantum information theory and graphical causal inference. It will also lead to exchange of important ideas between two currently disconnected communities of classical causal inference and foundational quantum information theory.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 18, 2020
- Source ID
- HR00112010008
Entities
People
- Jacob Zubin
Organizations
- Defense Advanced Research Projects Agency
- Purdue University