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Andrei Khrenikov

Publications and source records attributed to Andrei Khrenikov.

2 recordsLinked to original sources

Quantum-like Coherence Derived from the Interaction between Chemical Reaction and Its Environment

By uncovering the contrast between Artificial Intelligence and Natural-born Intelligence as a computational process, we define closed computing and open computing, and implement open computing within chemical reactions. This involves forming a mixture and invalidation of the computational process and the execution environment, which are logically distinct, and coalescing both to create a system that adjusts fluctuations. We model chemical reactions by considering the computation as the chemical reaction and the execution environment as the degree of aggregation of molecules that interact with the reactive environment. This results in a chemical reaction that progresses while repeatedly clustering and de-clustering, where concentration no longer holds significant meaning. Open computing is segmented into Token computing, which focuses on the individual behavior of chemical molecules, and Type computing, which focuses on normative behavior. Ultimately, both are constructed as an interplay between the two. In this system, Token computing demonstrates self-organizing critical phenomena, while Type computing exhibits quantum logic. Through their interplay, the recruitment of fluctuations is realized, giving rise to interactions between quantum logical subspaces corresponding to quantum coherence across different Hilbert spaces. As a result, spike waves are formed, enabling signal transmission. This occurrence may be termed quantum-like coherence, implying the source of enzymes responsible for controlling spike waves and biochemical rhythms.

cs.AI↗

Representation theorem for obsevables on a quantum logic

We study a conditional state on a quantum logic using Renyi's approach (or Bayesian principle). This approach helps us to define independence of events and differently from the situation in the classical theory of probability, if an event $a$ is independent of an event $b$, then the event $b$ can be dependent on the event $a$. We will show that we can define a $s$-map (function for simultaneous measurements on a quantum logic). It can be shown that if we have the conditional state we can define the $s$-map and conversely. By using the $s$-map we can introduce joint distribution also for noncompatible observables on a quantum logic.

quant-ph↗