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arXiv · 2511.13090

Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution

Arun Kumar Pati·Vlatko Vedral·Erik Sjoqvist
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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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Arun Kumar Pati, Vlatko Vedral, Erik Sjoqvist. 2025-11-24. Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution. https://arxiv.org/abs/2511.13090

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