arXiv:2603.23656 · Physics Letters A

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

T. Koide, A. van de Venn

quant-phcond-mat.stat-mechhep-thnucl-thSubmitted Mar 24, 2026• Announced Mar 26, 2026• 0 citations• Revised Aug 5, 2026 (v3)

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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.

Journal reference: Physics Letters A 594, 132074 (2026)
DOI: 10.1016/j.physleta.2026.132074
Comments: 25 pages, 6 figures. Title changed, references and discussions added. Accepted for publication in Phys. Lett. A

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