CHAPTER: INFORMATION THEORY — Linear and Nonlinear Quantum of Information

CHAPTER: INFORMATION THEORY — Linear and Nonlinear Quantum of InformationFigure 1 — Fourier Epicycles: Linear Description of the Quantum of Information> FOURIER EPICYCLES — LINEAR QUANTUM> Formula: , > Principle: A 2D path approximated by a sum of rotating circular modes.> > Information Theory Interpretation (Author's contribution):> One rotating circle = one quantum of information.> State of the quantum is defined by (amplitude and phase).> Any complex form is a linear superposition of quanta.> Example: quanta are required to encode a dragonfly with approximation error 0.95%.> When light is off, the form disappears: . This is volatile, linear memory.> This figure uses a well-known mathematical principle (Fourier, 1822) to illustrate the author's definition of a linear quantum.Caption for Zenodo:Figure 2 — FWA Square Window Memory: Nonlinear Quantum of Information> SILICON PHOTONIC CHIP — FWA SQUARE WINDOW MEMORY> Top View — Four-Wave Adiabatic Square Window Memory via Coupled Microring Resonators> > Device: SOI Photonic Platform, Silicon Waveguide 220nm SOI. Operation wavelength fin = fout = 1550 nm.> Structure: 4x Microring Resonators R = 20 μm (Ring A, B, C, D). Coupled orthogonally to a central node.> Physical Principle:> — zero-detuning dynamic interference state.> — constructive interference creates stable square memory window.> — Refractive index change in Si Device Layer (220nm) / SiO2 BOX Layer / Si Substrate. Light field is stored as material change.> > Information Theory Interpretation (Author's contribution):> This is the nonlinear quantum. While N=1536 linear quanta make a dragonfly, N=4 quanta interfere nonlinearly to create a stable SQUARE WINDOW.> The square is not just a sum, it is a self-consistent state: light creates the structure, structure holds the light.> When light is off, the imprint remains: . This is non-volatile photonic memory.> The square is the minimal code, the basic memory cell. The dragonfly is the complex code.Caption for Zenodo:Combined conclusion for Theory of Information:> Information Theory: From Linear to Nonlinear> Linear Quantum (Fig.1): Circle → Superposition → Volatile Image.> Nonlinear Quantum (Fig.2): 4 Circles → Interference at F=0* → Stable Square Window → Non-volatile Memory.> Any information can be encoded linearly. Only interference can store it.FWA. Kolesnikov Igor. Mark