Golden Ratio Absent in Dephasing-Optimal Transport Link — E8 Intelligence Research

Abstract

FINDING: The search results are tangential — they return general lectures on quantum dephasing channels and optimal transport theory, but **no specific paper or result linking dephasing rate to the golden ratio or optimal efficiency** is present. The only concrete mathematical content is the standard formalism of dephasing channels and Wasserstein distance. MATH: - Dephasing channel (from QC 9 lecture): \(\rho \mapsto (1-p)\rho + p Z\rho Z\), with dephasing rate \(\gamma = 1 - 2p\) (or \(p = \frac{1-\gamma}{2}\)). No golden ratio appears. - Wasserstein distance (from Cuturi lecture): \(W_p(\mu,\nu) = \left( \inf_{\pi \in \Pi(\mu,\nu)} \int \|x-y\|^p d\pi(x,y) \right)^{1/p}\). Regularized version adds entropy term \(-\lambda H(\pi)\). No golden ratio. - Nazarov's lecture: standard Lindblad master equation \(\dot{\rho} = -i[H,\rho] + \sum_k \gamma_k (L_k \rho L_k^\dagger - \frac{1}{2}\{L_k^\dagger L_k, \rho\})\). Dephasing rate \(\gamma_\phi\) is a free parameter, not derived as optima Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com