An Observation on the Structural Correspondences between Signal/Control Theory and Quantum Mechanics, Quantum Optics, and Open Quantum Systems

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.