Information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail. It is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the Shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process. When some measurement outcome is obtained, the decrease of the Shannon entropy of the measured system is compared with that of the von Neumann entropy. Furthermore, a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the Shannon entropy of the measured physical system.
This paper proposes the Information Entropy Physical Quantization (IEPQ) framework, a novel approach to understanding the physical nature of information entropy within the context of quantum systems. The core claim of IEPQ is that information entropy can be physically quantifiable and exhibits a fundamental correspondence with quantum states. The proposed mechanism leverages quantum information theory, mapping information entropy to the description of quantum states. Utilizing quantum measurement and entanglement, IEPQ seeks to achieve the physical manipulation and transformation of information entropy. This work delves into the mathematical formalization of this framework, outlining key concepts and potential applications, primarily focusing on the theoretical development rather than experimental validation. The goal is to establish a bridge between information theory and quantum physics, offering a new perspective on the relationship between information and reality at the fundamental level. ---
The concepts of conditional entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum systems. The fundamental difference between the classical case and the quantum one is that the entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and superdense coding are described and explained in terms of the generalized conditional entropy and information.