Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution

• URL: http://arxiv.org/abs/2511.13090v2
• Date: Mon, 24 Nov 2025 10:46:51 GMT
• Title: Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution
• Authors: Arun Kumar Pati, Vlatko Vedral, Erik Sjoqvist,
• Abstract summary: We prove a remarkably simple and universal law demonstrating that this partitioning is governed, at every instant, solely by a single geometric quantity.<n>This result provides a universally applicable and rigorous way to define the exact fraction of the total phase that is geometric versus dynamical in origin.<n>This finding has immediate practical consequences, furnishing a real-time measure of the geometricity of an evolution for designing high-fidelity geometric quantum gates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is governed, at every instant, solely by a single geometric quantity: the Bargmann angle (Bures angle). This result provides a universally applicable and rigorous way to define the exact fraction of the total phase that is geometric versus dynamical in origin, thereby establishing a new quantitative link between the dynamics of quantum evolution and the geometry of the state space. This finding has immediate practical consequences, furnishing a real-time measure of the geometricity of an evolution for designing high-fidelity geometric quantum gates with optimized robustness, and opening new avenues for quantum speed limit and coherent control.

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