Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909919242878976 |
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| author | Pati, Arun Kumar Vedral, Vlatko Sjoqvist, Erik |
| author_facet | Pati, Arun Kumar Vedral, Vlatko Sjoqvist, Erik |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution Pati, Arun Kumar Vedral, Vlatko Sjoqvist, Erik Quantum Physics Physics Education 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. |
| title | Fractional Contribution of Dynamical and Geometric Phases in Quantum Evolution |
| topic | Quantum Physics Physics Education |
| url | https://arxiv.org/abs/2511.13090 |