Holonomy and Complementarity in Open Quantum Systems

• URL: http://arxiv.org/abs/2605.10800v1
• Date: Mon, 11 May 2026 16:26:51 GMT
• Title: Holonomy and Complementarity in Open Quantum Systems
• Abstract summary: We show that complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems.<n>For a driven dissipative qubit, the complementarity variables define cylindrical coordinates on the Bloch sphere.<n>Openness appears geometrically as a radial deficit associated with reduction from a larger Hilbert space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems. Here we show that, in open quantum systems, these local constraints acquire a geometric interpretation through quasistatic transport. For a driven dissipative qubit, the complementarity variables define cylindrical coordinates on the Bloch sphere, while openness appears geometrically as a radial deficit associated with reduction from a larger Hilbert space. Quasistatic driving induces a work connection on the resulting steady-state manifold whose curvature determines the cyclic response. Hamiltonian-aligned dissipation produces an exact work connection and vanishing cyclic work, whereas fixed pointer-basis dissipation generates non-integrable transport, finite curvature, and holonomic response. The resulting curvature admits a phase-resolved representation on the triality manifold and develops perturbatively with pointer--Hamiltonian mismatch. In the weak-mismatch limit, the curvature is governed by a competition between coherence-preserving and pure-dephasing channels, producing symmetry-related positive- and negative-curvature sectors. These results establish a direct connection between complementarity, dissipation, and geometric thermodynamic response, and show that cyclic quasistatic work provides an operational probe of nonequilibrium quantum geometry.

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