Quantum Channel-Induced Geometry of the Uhlmann Phase in Qubit Systems

• URL: http://arxiv.org/abs/2608.11714v1
• Date: Wed, 12 Aug 2026 06:52:40 GMT
• Title: Quantum Channel-Induced Geometry of the Uhlmann Phase in Qubit Systems
• Abstract summary: We show that a qubit prepared in a pure state, which carries no geometric phase of its own, acquires a nontrivial Uhlmann phase.<n>The net topological charge of these defects is constrained to zero by the Poincaré--Hopf theorem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that a cyclically controlled non-coherence-generating channel supplies a two-parameter family of closed Bloch trajectories, absent in the single-parameter (temperature) cycles of the thermal Uhlmann literature, whose associated Uhlmann phase develops a genuine vortex--antivortex structure on the channel-parameter torus. A qubit prepared in a pure state, which carries no geometric phase of its own, acquires a nontrivial Uhlmann phase, obtained here in closed form, purely from a closed loop in the space of the native quantum channel parameters. The net topological charge of these defects is constrained to zero by the Poincaré--Hopf theorem. As the input-state orientation approaches its critical values, the defects merge and annihilate in pairs following a square-root coalescence law. This defect dynamics drives local geometric transitions, a mechanism that contrasts with single-parameter thermal Uhlmann transitions, where a global quantized winding jumps as a bulk invariant.

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