An Observation on the Structural Correspondences between Signal/Control Theory and Quantum Mechanics, Quantum Optics, and Open Quantum Systems
Abstract
Observation paper. This note juxtaposes ten structural correspondences, already present in the literature, between the mathematical structures of signal/control theory and those of quantum mechanics, quantum optics, and open quantum systems. Each item is classified as an exact mathematical identity (uncertainty principle; Wigner-Ville/Wigner distribution; Jones vector/qubit; SVD/Schmidt decomposition), a conditional exact isomorphism (paraxial/Schrodinger equation), a strong structural correspondence (sampling/phase-space degrees of freedom), or a structural parallel (state-space/Hilbert picture; observability/CSCO; Kalman filter/quantum filtering; dephasing/phase noise), with explicit limits. The note proposes no new interpretation, no new theorem, and no new prediction; its contribution is the juxtaposition and classification of known structures, with references only to classical original papers and standard textbooks. Japanese and English versions (md/tex/pdf) are included.
Fields of Study & Subjects
Quantum Mechanics and Applications
Quantum Information and Cryptography
Quantum and Classical Electrodynamics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 3 June 2026
- Language
- EN
- Document type
- Preprint