Information Theoretical Aspects of Quantum Mechanical Entropy

Shamba Dutta

I nformation is an idea created in human brain. But information has physical aspects too. Emergence of new theory and technology in physical science always contribute to shape various theories, models and services in LIS. Shannon’s mathematical formula derives strength from the physical aspect of data or information and gives a new information theoretic approach to communication model by introducing concepts of bit and entropy. With the advancement of Quantum mechanics a new quantum mechanical model is under preparation. Phenomenon like quantum entanglement is successfully being used in computer technology which in turn helps reshape many LIS services. Quantum information science is a newly flourishing field which is expected to bring great advancements in information organization, processing, retrieval, automatic classification, NLP and other LIS related problems.

Nilanjana Datta

Jincheng Zhang

This paper proposes a novel framework for understanding neuronal information processing, moving beyond the conventional emphasis on synaptic transmission. We hypothesize that neuronal information encoding relies fundamentally on the quantum entropy extracted from correlations between neurons, mediated by quantum entanglement. While synaptic transmission undoubtedly plays a role in facilitating information transfer, it is posited as a secondary mechanism supporting the primary quantum-based encoding process. We introduce a theoretical model leveraging the concept of quantum entanglement to describe how neuronal states are measured and how this measurement yields information that can be used to build a neuronal network's information processing model. The core idea is that the inherent quantum fluctuations within neurons, when coupled through entanglement, provide a source of information that can be quantified as entropy, forming the basis for neuronal communication. This approach challenges the prevailing view of neuronal information processing and opens new avenues for exploring the potential of quantum mechanics in biological systems. Mathematical formalism is presented to illustrate key aspects of this framework, focusing on entropy calculations and entanglement correlation analysis.

Progonov, Dmitro, Machusky, Eugene, Lucenko, Volodimir

Ryszard Horodecki, Michał Horodecki

Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the \ensuremath{\alpha} entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable 2\ifmmode\times\else\texttimes\fi{}2 systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional \ensuremath{\alpha} entropy is also emphasized. \textcopyright{} 1996 The American Physical Society.