Fundamental limits on state preparation for an open qubit

• URL: http://arxiv.org/abs/2607.04320v1
• Date: Sun, 05 Jul 2026 14:09:53 GMT
• Title: Fundamental limits on state preparation for an open qubit
• Abstract summary: We analytically determine the ultimate limits of state preparation in two-level open quantum systems driven by coherent control.<n>For a dissipative qubit governed by a GKSL master equation, we give an exact characterization of the reachable set in the Bloch ball.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analytically determine the ultimate limits of state preparation in two-level open quantum systems driven by coherent control. For a dissipative qubit governed by a GKSL master equation, we give an exact characterization of the reachable set in the Bloch ball. Dissipation excludes a region of states in the Bloch ball which cannot be approached even under arbitrarily strong coherent driving, and we prove that this region has a nontrivial geometry whose boundary is a surface of revolution around the $x$-axis which is analytic except for two conical singularities. We derive a closed-form control protocol for moving on this boundary, and construct an explicit protocol that steers the system arbitrarily close to any prescribed boundary state. These results provide a complete geometric constructive description of reachable qubit states in the standard dissipative environment, establishing fundamental bounds on controllability and state-preparation fidelity for open two-level quantum systems.

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