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arXiv:quant-ph/9906037

Quantum Measured Information

Yi-Xin Chen

Published Jun 12, 1999• 0 citations
arXivHTMLPDF

Abstract

A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured system and "pointer" states of measuring apparatus, which is generated by dynamical process of quantum measurement, plays a dominant role in expressing quantum characteristics of information theory. The quantum mutual information of transmission and reception of quantum states along a noisy quantum channel is given by the change of quantum measured information. In our approach, it is not necessary to purify the transmitted state by means of the reference system. It is also clarified that there exist relations between the approach given in this letter and those given by other authors.

DOI
10.48550/arxiv.quant-ph/9906037

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A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured system and "pointer" states of measuring apparatus, which is generated by dynamical process of quantum measurement, plays a dominant role in expressing quantum characteristics of information theory. The quantum mutual information of transmission and reception of quantum states along a noisy quantum channel is given by the change of quantum measured information. In our approach, it is not necessary to purify the transmitted state by means of the reference system. It is also clarified that there exist relations between the approach given in this letter and those given by other authors.
Quantum and classical informations are considered in quantum measurement processes described by pure operations. The quantum information is given by coherent information in the state change of the measured physical system, and the classical information represented by the Shannon mutual information is obtained from the measurement outcomes. It is shown that if the maximum classical information is obtained, the quantum information becomes zero and if any classical information is not obtained, all the quantum information that the physical system has can be transmitted.
Quantum Information Theory (QIT) has emerged as one of the most influential fields in modern science, combining the principles of quantum mechanics with classical information theory. It forms the theoretical foundation of advanced technologies such as quantum computing, quantum communication, and quantum cryptography. Despite remarkable progress in these areas, the measurement problem remains a fundamental conceptual and practical challenge. Measurement in quantum mechanics plays a dual role: it enables information extraction while simultaneously disturbing the quantum system. This paper presents a detailed study of the measurement problem within the framework of quantum information theory. It examines the role of measurement in quantum state evolution, the effects of entanglement and decoherence, and the impact on information processing tasks. The paper also discusses existing theoretical approaches and highlights the importance of resolving measurement-related issues for the future development of quantum technologies.
This chapter sets the basis of quantum information theory (QIT) . The central purpose of QIT is to qualify the transmission of either classical or quantum information over quantum channels . The starting point of the QIT description is von Neumann entropy , S (ρ), which represents the quantum counterpart of Shannon's classical entropy, H ( X ). Such a definition rests on that of the density operator (or density matrix ) of a quantum system, ρ, which plays a role similar to that of the random-events source X in Shannon's theory. As we shall see, there also exists an elegant and one-to-one correspondence between the quantum and classical definitions of the entropy variants relative entropy , joint entropy , conditional entropy , and mutual information . But such a similarity is only apparent. Indeed, one becomes rapidly convinced from a systematic analysis of the entropy's additivity rules that fundamental differences separate the two worlds. The classical notion of information correlation between two event sources for quantum states shall be referred to as quantum entanglement . We then define a quantum communication channel, which encodes and decodes classical information into or from quantum states. The analysis shows that the mutual information H ( X ; Y ) between originator and recipient in this communication channel cannot exceed a quantity χ, called the Holevo bound , which itself satisfies χ ≤ H ( X ), where H ( X ) is the entropy of the originator's classical information source.
The kind of information provided by a measurement is determined in terms of the correlation established between observables of the apparatus and the measured system. Using the framework of quantum measurement theory, necessary and sufficient conditions for a measurement interaction to produce strong correlations are given and are found to be related to properties of the final object and apparatus states. These general results are illustrated with reference to the standard model of the quantum theory measurement.
Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a new set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.
This paper explores a novel extension of information theory, focusing on the concept of "information content" as a dynamic system-level property rather than simply a probabilistic outcome. We propose a framework that leverages quantum entanglement to encode and transmit information, moving beyond classical probability-based approaches. This theory emphasizes the crucial role of quantum state structure and interaction in defining and quantifying information. The core mechanism centers on a shift from probability description to an information-driven description, introducing the concept of "information resonance" within quantum states. This expansion addresses a fundamental limitation of existing quantum information theory by providing a more holistic and physically meaningful perspective on information encoding and transmission, potentially offering new avenues for quantum technologies.