Information-Geometric Quantum Process Tomography of Single Qubit Systems

Quantum Physics [Submitted on 24 Mar 2026] Information-Geometric Quantum Process Tomography of Single Qubit Systems T. Koide, A. van de Venn We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an extension of thermodynamic speed limits, which are typically formulated as inequalities. For single qubits, we show that this inequality saturates into a strict equality because the density matrix belongs to the quantum exponential family, with the Pauli matrices serving as sufficient statistics. From a practical perspective, this identity enables a non-iterative linear regression approach to continuous-time quantum process tomography, bypassing the local minima issues common in non-linear optimization. We demonstrate the efficiency of this method by estimating the Hamiltonian and dissipation parameters of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. Numerical simulations confirm the validity of this geometric estimator and highlight the necessity of error mitigation near the pure-state boundary where the inverse metric becomes singular. Comments: 23 pages, 6 figures Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Nuclear Theory (nucl-th) Cite as: arXiv:2603.23656 [quant-ph]   (or arXiv:2603.23656v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.23656 Focus to learn more Submission history From: Tomoi Koide [view email] [v1] Tue, 24 Mar 2026 18:59:59 UTC (588 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech hep-th nucl-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)