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arXiv · 2607.04320

Fundamental limits on state preparation for an open qubit

D. A. Abraamian·L. V. Lokutsievskiy·A. N. Pechen
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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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D. A. Abraamian, L. V. Lokutsievskiy, A. N. Pechen. 2026-07-05. Fundamental limits on state preparation for an open qubit. https://arxiv.org/abs/2607.04320

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