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Translations of mathematical monographs

Information geometry for quantum systems

Amari, Shun-ichi, Nagaoka, Hiroshi

Published Apr 13, 2007• 2 citations
Publisher
DOI
10.1090/mmono/191/07

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Review of Comparative Geometric Analysis of a Qubit and an RLC Circuit under Time-Embedded and Group-Theoretic Information Geometries

Syed Muntasir Mamun

This review examines the paper by Tomonori Yoshino (2023) on the comparative geometric analysis of a classical RLC circuit and a quantum two-level system (qubit) using two frameworks: group-theoretic information geometry and time-embedded information geometry (TEIG). The original work postulates structural analogies between classical dissipation and quantum decoherence, hypothesizing that TEIG better captures time-dependent and non-Markovian dynamics while group-theoretic geometry excels in symmetry representation. Key results highlight TEIG's ability to incorporate temporal embedding and rupture dynamics, suggesting a unified perspective for classical and quantum systems. Algebraic interpretations involve Lie group actions and time-dependent metrics, while geometric views emphasize manifolds like the Bloch sphere and phase spaces. Secondary research reveals similar efforts in circuit quantum electrodynamics (cQED) and quantum information geometry, indicating ongoing progress toward hybrid classical-quantum models. This review synthesizes these elements, evaluates hypotheses, and discusses future directions in unifying geometric descriptions of physical information systems. Mamun, SM (2026)…………………………………………1 Review of Comparative Geometric Analysis of a Qubit and an RLC Circuit under Time-Embedded and Group-Theoretic Information Geometries Also available on Academia.edu: https://www.academia.edu/attachments/131996529/download_file?s=portfolio

•Jan 1, 2026•0 citations

Quantum Information Geometry and Quantum Estimation

Springer eBooks•Sep 1, 2006•0 citations
This review examines the paper by Tomonori Yoshino (2023) on the comparative geometric analysis of a classical RLC circuit and a quantum two-level system (qubit) using two frameworks: group-theoretic information geometry and time-embedded information geometry (TEIG). The original work postulates structural analogies between classical dissipation and quantum decoherence, hypothesizing that TEIG better captures time-dependent and non-Markovian dynamics while group-theoretic geometry excels in symmetry representation. Key results highlight TEIG's ability to incorporate temporal embedding and rupture dynamics, suggesting a unified perspective for classical and quantum systems. Algebraic interpretations involve Lie group actions and time-dependent metrics, while geometric views emphasize manifolds like the Bloch sphere and phase spaces. Secondary research reveals similar efforts in circuit quantum electrodynamics (cQED) and quantum information geometry, indicating ongoing progress toward hybrid classical-quantum models. This review synthesizes these elements, evaluates hypotheses, and discusses future directions in unifying geometric descriptions of physical information systems. Mamun, SM (2026)…………………………………………1 Review of Comparative Geometric Analysis of a Qubit and an RLC Circuit under Time-Embedded and Group-Theoretic Information Geometries Also available on Academia.edu: https://www.academia.edu/attachments/131996529/download_file?s=portfolio