Dynamics of conditional mutual information in thermalization

Quantum thermalization is a fundamental phenomenon of quantum many-body systems, and understanding the correlational structure of quantum states during this process is key to uncovering the mechanisms of thermalization. Conditional mutual information (CMI) serves as a powerful tool in this context. While previous studies have demonstrated that in thermal equilibrium (Gibbs) states, CMI decays exponentially with distance for local Hamiltonians above a certain temperature, less is known about the behavior of CMI in intermediate, non-equilibrium states during thermalization. Recent work [1] on random circuits coupled to an infinite temperature bath reveals that these intermediate states can exhibit long-range CMI, distinct from Gibbs states. Motivated by these findings, we explore the evolution of CMI across various thermalization processes, providing insights into the dynamics of correlations in quantum systems out of equilibrium.

[1] S. Lee, C. Oh, Y. Wong, S. Chen, and L. Jiang, Universal Spreading of Conditional Mutual Information in Noisy Random Circuits, (2024), arXiv:2402.18548. (accepted in PRL)