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arXiv:1303.0777

Integrating hidden information which is observed and the observer information regularities

Vladimir S. Lerner

Published Mar 4, 2013• 1 citation
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Abstract

Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles conjugated fractions in microprocess, enclosing the captured entropy fractions as source of an information unit. The impulse step-up action launches the unit formation and step-down action finishes it and brings energy from the interactive jump. This finite jump transfers the entangled entropy from uncertain Yes-logic to the certain-information No-logic information unit whose measuring at end of the cut kills final entropy-uncertainty and limits unit. The Yes-No logic holds Bit Participator creating elementary information observer without physical pre-law. Cooperating two units in doublet and an opposite directional information unit in triplet forms minimal stable structure. Information path functional (IPF) integrates multiple hidden information contributions along the cutting process correlations in information units of cooperating doublets-triplets, bound by free information, and enfolds the sequence of enclosing triplet structures in the information network (IN) that sequentially decreases the entropy and maximizes information. The IN bound triplets release free information rising information forces enable attracting new information unit and ordering it. While IPF collects the information units, the IN performs logical computing using doublet-triplet code. The IN different levels unite logic of quantum micro- and macro- information processes, composing quantum and/or classical computation.

DOI
10.48550/arxiv.1303.0777

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Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles conjugated fractions in microprocess, enclosing the captured entropy fractions as source of an information unit. The impulse step-up action launches the unit formation and step-down action finishes it and brings energy from the interactive jump. This finite jump transfers the entangled entropy from uncertain Yes-logic to the certain-information No-logic information unit whose measuring at end of the cut kills final entropy-uncertainty and limits unit. The Yes-No logic holds Bit Participator creating elementary information observer without physical pre-law. Cooperating two units in doublet and an opposite directional information unit in triplet forms minimal stable structure. Information path functional (IPF) integrates multiple hidden information contributions along the cutting process correlations in information units of cooperating doublets-triplets, bound by free information, and enfolds the sequence of enclosing triplet structures in the information network (IN) that sequentially decreases the entropy and maximizes information. The IN bound triplets release free information rising information forces enable attracting new information unit and ordering it. While IPF collects the information units, the IN performs logical computing using doublet-triplet code. The IN different levels unite logic of quantum micro- and macro- information processes, composing quantum and/or classical computation.
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy. Each inter action models Kronicker impulse, delta impulse models interaction between the Kronicker impulses. Each impulse step down action cuts maximum of impulse minimal entropy and impulse step up action transits cutting minimal entropy to each step up action of merging delta function. Delta step down action kills delivering entropy producing equivalent minimax information. The merging action initiates quantum microprocess. Multiple cutting entropy is converting to information micro macroprocess. Cutting impulse entropy integrates entropy functional EF along trajectories of multidimensional diffusion process. Information which delivers ending states of each impulse integrates information path functional IPF along process trajectories. Hidden information evaluates Feller kernel whose minimal path transforms Markov transition probability to probability of Brownian diffusion. Each transitive transformation virtually observes origin of hidden information probabilities correlated states. IPF integrates observing Bits along minimal path assembling information Observer. Minimax imposes variation principle on EF and IPF whose extreme equations describe observing micro and macroprocess which describes irreversible thermodynamics. Hidden information curries free information frozen from correlated connections. Free information binds observing micro macro processes in information macrodynamics. Each dynamic three free information composes triplet structures. Three structural triplets assemble information network. Triple networks free information cooperate information Observer.
Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses processing the interactions in observable process. The impulse observation increases each posteriori correlation reducing conditional entropy measures from finite uncertainty up to certainty of real impulse. The reduced entropy conveys probabilistic causality with time course and temporal memory in collecting correlations, which interactive impulse innately cuts exposing hidden process entropy. The natural cut of this entropy reveals information hidden in the correlation connections. Inside the merging probing impulse emerges reversible microprocess with yes-no conjugated entangled entropy, curvature and logical complexity. Within the impulse time interval, entanglement starts before its space is formed and ends with beginning the space during reversible relative time interval being small part of impulse time interval. Merging impulse curves and rotates the impulse interactive actions in microprocess whose space interval measures this transitive movement.The cutting entropy sequentially converting to information memorizes the probes logic in Bit, participating in next probe conversions and encoding which memorizes information causality. The complexity and mass appears after the space emerges from the entanglement.The cognition assembles common units through the multiple attraction and resonances at forming network (IN) of triplet hierarchy, which accept only units that concentrates and recognizes each triplet IN node. The ended triplet of hierarchical INs measures level of the observer intelligence. The synthesized optimal process minimizes the observations time in Artificial designed information Observer with intellectual searching logic.
What is information originating in observation? Until now it has no scientifically conclusive definition. Information is memorized entropy cutting in random observations which processing interactions. Randomness of various interactive observations is source of entropy as uncertainty. Observation under random 1-0 impulses probabilities reveals hidden correlation which connects Bayesian probabilities increasing each posterior correlation. That sequentially reduces relational entropy conveying probabilistic casualty with temporal memory of correlations which interactive impulse innately cuts. Within hidden correlation emerges reversible time space microprocess with conjugated entangled entropy which probing impulse intentionally cuts and memorizes information as certainty. Sequential interactive cuts integrates cutting information in information macroprocess with irreversible time course. Memorized information binds reversible microprocess within impulse with irreversible information macroprocess. Observer probes collect cutting information data bits of observing frequencies impulses. Each impulse cuts maximum of impulse minimal information performing dual max-min principle of converting process entropy to information through uncertain gap. Multiple naturally encoding bits moving in macroprocess join triplet macrounits which logically organize information networks encoding macrounits in structures enclosing triplet code. Network time space distributed structure self renews and cooperates information decreasing its complexity. Integrating process entropy functional and bits information in information path integral embraces variation minimax law which determines processes regularities. Solving problem mathematically describes micro macro processes, network, and invariant conditions of observer network self replication.
Up to now both information and its connection to reality have not scientifically conclusive definitions neither implicit origin. They emerge in observing multiple impulses interactive yes-no actions modeling information Bits. The observed information process connects reality, information, and creates Observer. Interaction is fundamental reality building structure of Universe from quantum physics up to brain neurons interactive actions. Merging action and reaction joins probabilistic prior and posterior actions on edge of the observed predictability and begins microprocess. Its time of entanglement starts space interval composing two qubits or Bit of reversible logic in the emerging information process. The impulse interacting action curves impulse geometry creating asymmetrical logic Bit as logical Maxwell demon. With approaching probability one, the attracting interaction captures energy memorizing asymmetrical logic in information certain Bit. Such Bit is naturally extracted at minimal quality energy equivalent ln2 working as Maxwell Demon. The memorized impulse Bit and its free information self-organizes multiple Bits in triplets sructuring macroprocess. Memorized information binds reversible microprocess with irreversible information macroprocess along multidimensional observing process. The macroprocess self-forming triplet units UP attract new UP through free Information. Multiple UP adjoin hierarchical network whose free information produces new UP at higher level node and encodes triplets in multi-levels hierarchical organization. The interactive information dynamics assemble geometrical and information structures of cognition and intelligence in double spiral rotating code. Information Path Functional integrates multiple interactive dynamics in finite bits which observe and measure reality. The time and space of reality exists only as units of information as Wheeler predicted.
We study a polynomial-time decision problem in which each input encodes a depth-NNN causal execution in which a single non-duplicable token must traverse an ordered sequence of steps, revealing at most O(1)O(1)O(1) bits of routing information at each step. The uncertainty in the problem lies in identifying the delivery path through the relay network rather than in the final accept/reject outcome, which is defined solely by completion of the prescribed execution. A deterministic Turing machine executes the process in Θ(N)Θ(N)Θ(N) time. Using information-theoretic tools - specifically cut-set bounds for relay channels and Fano's inequality - we prove that any execution respecting the causal constraints requires Ω(N)Ω(N)Ω(N) units of causal time, thereby ruling out asymptotic parallel speedup. We further show that no classical NC\mathbf{NC}NC circuit family can implement the process when circuit depth is interpreted as realizable parallel time. This identifies a class of polynomial-time problems with intrinsic causal structure and highlights a gap between logical parallelism and causal executability.
La théorie de l'information quantique s'est développée à une vitesse fulgurante au cours des vingt dernières années, avec des analogues et extensions des théorèmes de codage de source et de codage sur canal bruité pour la communication unidirectionnelle. Pour la communication interactive, un analogue quantique de la complexité de la communication a été développé, pour lequel les protocoles quantiques peuvent performer exponentiellement mieux que les meilleurs protocoles classiques pour certaines tâches classiques. Cependant, l'information quantique est beaucoup plus sensible au bruit que l'information classique. Il est donc impératif d'utiliser les ressources quantiques à leur plein potentiel. Dans cette thèse, nous étudions les protocoles quantiques interactifs du point de vue de la théorie de l'information et étudions les analogues du codage de source et du codage sur canal bruité. Le cadre considéré est celui de la complexité de la communication: Alice et Bob veulent faire un calcul quantique biparti tout en minimisant la quantité de communication échangée, sans égard au coût des calculs locaux. Nos résultats sont séparés en trois chapitres distincts, qui sont organisés de sorte à ce que chacun puisse être lu indépendamment. Étant donné le rôle central qu'elle occupe dans le contexte de la compression interactive, un chapitre est dédié à l'étude de la tâche de la redistribution d'état quantique. Nous prouvons des bornes inférieures sur les coûts de communication nécessaires dans un contexte interactif. Nous prouvons également des bornes atteignables avec un seul message, dans un contexte d'usage unique. Dans un chapitre subséquent, nous définissons une nouvelle notion de complexité de l'information quantique. Celle-ci caractérise la quantité d'information, plutôt que de communication, qu'Alice et Bob doivent échanger pour calculer une tâche bipartie. Nous prouvons beaucoup de propriétés structurelles pour cette quantité, et nous lui donnons une interprétation opérationnelle en tant que complexité de la communication quantique amortie. Dans le cas particulier d'entrées classiques, nous donnons une autre caractérisation permettant de quantifier le coût encouru par un protocole quantique qui oublie de l'information classique. Deux applications sont présentées: le premier résultat général de somme directe pour la complexité de la communication quantique à plus d'une ronde, ainsi qu'une borne optimale, à un terme polylogarithmique près, pour la complexité de la communication quantique avec un nombre de rondes limité pour la fonction « ensembles disjoints ». Dans un chapitre final, nous initions l'étude de la capacité interactive quantique pour les canaux bruités. Étant donné que les techniques pour distribuer de l'intrication sont bien étudiées, nous nous concentrons sur un modèle avec intrication préalable parfaite et communication classique bruitée. Nous démontrons que dans le cadre plus ardu des erreurs adversarielles, nous pouvons tolérer un taux d'erreur maximal de une demie moins epsilon, avec epsilon plus grand que zéro arbitrairement petit, et ce avec un taux de communication positif. Il s'ensuit que les canaux avec bruit aléatoire ayant une capacité positive pour la transmission unidirectionnelle ont une capacité positive pour la communication interactive quantique. Nous concluons avec une discussion de nos résultats et des directions futures pour ce programme de recherche sur une théorie de l'information quantique interactive.