Information-Geometric Quantum Process Tomography in Unital Open Single-Qubit Dynamics

Abstract:We derive an exact information-geometric inequality valid for both Markovian and non-Markovian mixed-state dynamics. This inequality saturates into a strict equality for single qubits because they belong to the quantum exponential family. This identity enables a non-iterative linear regression approach to continuous-time quantum process tomography, which, provided the full-rank condition is satisfied, yields a unique global solution and avoids local minima traps typical of standard non-linear optimization. Furthermore, as the formulation is inherently unconstrained, negative dissipation rates provide direct evidence of non-Markovianity. Numerical simulations of the unital diagonal Bloch generator derived from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation demonstrate the validity of this geometric estimator and highlight the necessity of error mitigation near the pure-state boundary where the inverse metric becomes singular.

25 pages, 6 figures. Title changed, references and discussions added. Accepted for publication in Phys. Lett. A

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Nuclear Theory (nucl-th)

arXiv:2603.23656 [quant-ph]

(or arXiv:2603.23656v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.23656 Focus to learn more arXiv-issued DOI via DataCite

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