Probability-Phase Mutual Information

• URL: http://arxiv.org/abs/2510.01104v3
• Date: Thu, 23 Oct 2025 15:58:21 GMT
• Title: Probability-Phase Mutual Information
• Authors: Cameron Hahn, Nishan Ranabhat, Fabio Anza,
• Abstract summary: We introduce the probability-phase mutual information $I(P;Phi)$.<n>We show that it characterizes quantum coherence at the ensemble level.<n>Its relevance for quantum thermodynamics and deep thermalization in condensed matter physics is highlighted.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum coherence, is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce the same mixed state through different distributions of pure states. Building on the geometric formulation of quantum mechanics, we introduce the probability-phase mutual information $I(P;\Phi)$. We show that it characterizes quantum coherence at the ensemble level and that ensemble coherence systematically exceeds density-matrix coherence, thus quantifying the structure lost when averaging over pure states. Eventually, its relevance for quantum thermodynamics and deep thermalization in condensed matter physics is highlighted by explicit examples: canonical ensembles reveal temperature-dependent probability-phase correlations absent from thermal density matrices, while a non-vanishing $I(P;\Phi)$ signals the breakdown of deep thermalization.

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