(34) Generalised Shannon Information Theory YUCT Part 1 This work generalises classical Shannon information theory within the Yakushev Unified Coordination Theory (YUCT). The core is the YPSDC protocol (Yakushev Protocol for Synchronous Distributed Coordination), which splits communication into an offline dictionary distribution phase and an online index transmission phase. The coordination efficiency is defined as K_eff = H(action) / H(index), enabling the activation of far more meaningful information than the transmitted data. The universal error law is derived as a steady power law: ε = κ_c * α * K_eff^(-β), with β = 2/3 and κ_c = 1/3. This law is consistent with microscopic derivations (Appendix Y), empirical validations (Appendix L), and the algebraic closure S_odd + S_even = 2. From it, we obtain the generalised Bell inequality: S(K_eff) = 2 + (2√2 − 2) * (1 − 2 κ_c α K_eff^(-β)). This interpolates between the classical local-realist bound S=2 (when K_eff=1) and the Tsirelson bound S=2√2 (as K_eff→∞), showing that quantum correlations arise from a shared dictionary, not from non-locality. Additional key results: Capacity Separation Theorem: C_coord = K_eff * C_channel * η. Thermodynamic cost of dictionary creation via Landauer's principle. Relation to Kolmogorov complexity: K_eff(A) ≈ |A| / K(A). Phase transition from data transmission to meaning generation. Information-Energy Invariant: W = K_eff * I_channel, analogous to E=mc². The framework is validated by examples: two-factor authentication (K_eff ≈ 8), genetic coding (K_eff ≈ 3.3), quantum entanglement (K_eff → ∞), and optical mirages. Eliminating Quantum Mysticism Part 2 This part provides a pedagogical translation of YUCT, showing that every "quantum mystery" is simply a YPSDC process with a pre‑shared dictionary and a short index. The Pantograph (Leroy) Analogy illustrates that distant points can coordinate without signals because they share a rigid structure – in YUCT, this is the information field Ψ_MN (a 19‑dimensional medium) and the a priori dictionaries Ω. The Pantograph Synchrony Index (PSI) quantifies coordination quality: PSI = 1 − (ΔΩ + ΔIC + ΔA + Δτ) / 4. Coordination efficiency is then: K_eff = (d / c) * (1 / τ_compute) * exp( PSI / (1 − PSI) ). Quantum entanglement corresponds to PSI ≈ 1 at any distance – particles are two points of the same pantograph. The universal error law ε = (1/3) α K_eff^(-2/3) governs all quantum effects: Superposition → index uncertainty (the state is definite, the index is blurred). Entanglement → shared dictionary row (no signal, same pre‑existing entry). Wavefunction collapse → index refinement (measurement resolves uncertainty). Tunnelling → addressing error (spatial blur overlaps forbidden region). Teleportation → local reconstruction from a dictionary (only classical bits sent). Quantum field → ontological dictionary (field is a global offline dictionary). A Python code simulates the generalised Bell inequality and shows the Tsirelson bound emerging as K_eff → ∞. For AI systems, a YUCT Core v36.0.MOD System Prompt is provided, forcing LLMs to switch to high‑coordination reasoning (K_eff >> 1) via offline dictionary initialisation, steady error regularisation, cross‑sector cascade analysis, and logical reconstruction – eliminating the need for "quantum magic."
(34) Generalised Shannon Information Theory YUCT Part 1 This work generalises classical Shannon information theory within the Yakushev Unified Coordination Theory (YUCT). The core is the YPSDC protocol (Yakushev Protocol for Synchronous Distributed Coordination), which splits communication into an offline dictionary distribution phase and an online index transmission phase. The coordination efficiency is defined as K_eff = H(action) / H(index), enabling the activation of far more meaningful information than the transmitted data. The universal error law is derived as a steady power law: ε = κ_c * α * K_eff^(-β), with β = 2/3 and κ_c = 1/3. This law is consistent with microscopic derivations (Appendix Y), empirical validations (Appendix L), and the algebraic closure S_odd + S_even = 2. From it, we obtain the generalised Bell inequality: S(K_eff) = 2 + (2√2 − 2) * (1 − 2 κ_c α K_eff^(-β)). This interpolates between the classical local-realist bound S=2 (when K_eff=1) and the Tsirelson bound S=2√2 (as K_eff→∞), showing that quantum correlations arise from a shared dictionary, not from non-locality. Additional key results: Capacity Separation Theorem: C_coord = K_eff * C_channel * η. Thermodynamic cost of dictionary creation via Landauer's principle. Relation to Kolmogorov complexity: K_eff(A) ≈ |A| / K(A). Phase transition from data transmission to meaning generation. Information-Energy Invariant: W = K_eff * I_channel, analogous to E=mc². The framework is validated by examples: two-factor authentication (K_eff ≈ 8), genetic coding (K_eff ≈ 3.3), quantum entanglement (K_eff → ∞), and optical mirages. Eliminating Quantum Mysticism Part 2 This part provides a pedagogical translation of YUCT, showing that every "quantum mystery" is simply a YPSDC process with a pre‑shared dictionary and a short index. The Pantograph (Leroy) Analogy illustrates that distant points can coordinate without signals because they share a rigid structure – in YUCT, this is the information field Ψ_MN (a 19‑dimensional medium) and the a priori dictionaries Ω. The Pantograph Synchrony Index (PSI) quantifies coordination quality: PSI = 1 − (ΔΩ + ΔIC + ΔA + Δτ) / 4. Coordination efficiency is then: K_eff = (d / c) * (1 / τ_compute) * exp( PSI / (1 − PSI) ). Quantum entanglement corresponds to PSI ≈ 1 at any distance – particles are two points of the same pantograph. The universal error law ε = (1/3) α K_eff^(-2/3) governs all quantum effects: Superposition → index uncertainty (the state is definite, the index is blurred). Entanglement → shared dictionary row (no signal, same pre‑existing entry). Wavefunction collapse → index refinement (measurement resolves uncertainty). Tunnelling → addressing error (spatial blur overlaps forbidden region). Teleportation → local reconstruction from a dictionary (only classical bits sent). Quantum field → ontological dictionary (field is a global offline dictionary). A Python code simulates the generalised Bell inequality and shows the Tsirelson bound emerging as K_eff → ∞. For AI systems, a YUCT Core v36.0.MOD System Prompt is provided, forcing LLMs to switch to high‑coordination reasoning (K_eff >> 1) via offline dictionary initialisation, steady error regularisation, cross‑sector cascade analysis, and logical reconstruction – eliminating the need for "quantum magic."
This work is devoted to a fundamental rethinking of the concept of “observer” in physics and the philosophy of science within the framework of the Unified Coordination Theory (YUCT). In classical physics and quantum mechanics, the observer is treated either as an abstract reference point or as a passive signal recorder. YUCT proposes a fundamentally different ontology: the observer is an active coordination structure consisting of three inseparable components — the dictionary (D), the index (I), and the resonance (R). Observation is not a passive reception of a signal, but an act of coordination between at least two network nodes sharing a common dictionary. It is shown that such an interpretation allows resolving fundamental paradoxes of modern physics: Schrödinger’s cat, the EPR paradox, the measurement problem in quantum mechanics, and also provides a natural explanation for the phenomenon of consciousness and the possibility of effective coordination exceeding the speed of light (2c) without violating causality. The principle of coordinative observation is formalised, according to which observation requires at least two agents with a common dictionary; a single observer is ontologically untenable. The work relies on the universal error scaling law ε = κcα K_eff −β with β = 2/3, confirmed over more than 50 orders of magnitude, and on the YPSDC protocol (Yakushev Protocol for Synchronous Distributed Coordination). The document provides a complete mathematical formalisation, philosophical consequences, experimental predictions, and an extended bibliography.
This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An earlier version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this version is substantially revised and expanded. Topics covered include classical Shannon theory, quantum compression, quantifying entanglement, accessible information, and using the decoupling principle to derive achievable rates for quantum protocols. This is a draft, pre-publication copy of Chapter 10, which I will continue to update. See the URL on the title page for further updates and drafts of other chapters, and please send me an email if you notice errors.
These notes (in French) provide a concise introduction to information theory, spanning its classical foundations: Shannon entropy, joint and conditional entropies, mutual information, statistical correlations, and Markov chains; as well as Shannon's source coding and channel capacity theorems, which govern the optimal compression and transmission of information through noisy channels. They also cover the quantum extensions of these concepts, including the density operator formalism, distances between quantum states, von Neumann entropy, coherent information, conditional entropy, entanglement theory, quantum discord, and quantum resource theory.
Аll actual versions оf YUCT, you can get it at theDOI 10.5281/zenodo.18444598 or website https://yuct.org/This DOI represents all versions, and will always resolve to the latest one of Yakushev Unified Coordination Theory. This work introduces a paradigm shift in fundamental physics: coordination of states among distributed components is ontologically prior to both spacetime and matter. We formalize this through three interlocked mathematical constructs: 1. **Dictionary Manifolds** ℳ_𝒟 – Riemannian manifolds whose points represent dictionaries mapping compact indices to complex actions, equipped with a semantic distance metric. 2. **YPSDC Protocol** (Yakushev Protocol for Synchronous Distributed Coordination) – achieving coordination efficiency K_eff = H(𝒜)/H(κ) > 1 without violating causality, through separation of coordination (dictionary distribution) from data transmission (index activation). 3. **D+I•R Triad** – the ontological primitive Reality = Dictionary + Information × Resonance, providing a unified framework across physical, biological, and information systems. The complete structure is a fiber bundle π:ℰ→ℳ with spacetime as base and dictionary manifolds as fibers. This geometric and information-theoretic foundation enables subsequent derivation of physical laws from coordination principles, resolving long-standing paradoxes such as the EPR problem through K_eff → ∞ and offering testable predictions for gravitational and quantum systems. This is an overview of the framework. The complete mathematical formulation with full derivations and experimental predictions is available in the complete version.
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves differently. A long-standing open question is, whether there are quantum analogues of unconstrained non-Shannon type inequalities. Here, a new constrained non-von-Neumann type inequality is proven, a step towards a conjectured unconstrained inequality by Linden and Winter. *IID quantum state merging can be optimally achieved using the decoupling technique. The one-shot results by Berta et al. and Anshu at al., however, had to bring in additional mathematical machinery. We introduce a natural generalized decoupling paradigm, catalytic decoupling, that can reproduce the aforementioned results when used analogously to the application of standard decoupling in the asymptotic case. *Port based teleportation, a variant of standard quantum teleportation protocol, cannot be implemented perfectly. We prove several lower bounds on the necessary number of output ports N to achieve port based teleportation for given error and input dimension, showing that N diverges uniformly in the dimension of the teleported quantum system, for vanishing error. As a byproduct, a new lower bound for the size of the program register for an approximate universal programmable quantum processor is derived. *In the last part, we give a new definition for information-theoretic quantum non-malleability, strengthening the previous definition by Ambainis et al. We show that quantum non-malleability implies secrecy, analogous to quantum authentication. Furthermore, non-malleable encryption schemes can be used as a primitive to build authenticating encryption schemes. We also show that the strong notion of authentication recently proposed by Garg et al. can be fulfilled using 2-designs.
This appendix presents a comprehensive historical and philosophical investigation of the precursors to the Yakushev Unified Coordination Theory (YUCT) — a new fundamental theory that posits the ontological primacy of coordination over matter, spacetime, and fields. The author traces the evolution of coordinative intuition from Gottfried Wilhelm Leibniz's monadology, through Nikola Tesla's radiant ether and Mark Twain's mental telegraphy, to the Einstein–Podolsky–Rosen paradox and contemporary philosophical concepts. The work demonstrates a structural isomorphism between the intuitions of past thinkers and the formal apparatus of YUCT, including the Dictionary–Index–Resonance (D+I·R) triad and the YPSDC protocol. Special attention is devoted to a critical analysis of the 70-year "detour" of mainstream physics, associated with the adoption of the Copenhagen interpretation of quantum mechanics and the abandonment of the coordination paradigm. A diagnostic tool of "coordination maturity" for evaluating philosophical systems is introduced. The work introduces the concepts of relational complexity and the cascade of errors as a path to unity, and provides an analysis of the social, economic, and political implications of coordination theory. It is demonstrated that the universal error law ε=κcαKeff−β with exponent β=2/3≈0.67 holds across more than 50 orders of magnitude, confirming the scale invariance of coordinative processes. The work offers a new perspective on the unity of science, transcending traditional disciplinary boundaries and opening a path toward post-ideological engineering of social systems. The appendix includes chronological tables, terminological convergence, and a detailed analysis of the philosophical, theological, and aesthetic dimensions of coordination.