Quantum Information Entropy: A Generalized Definition

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper introduces a generalized definition of quantum information entropy, aiming to provide a more comprehensive framework for quantifying information in complex quantum systems. The core of this work lies in extending the conventional concept of entropy, traditionally applied to classical information, to the realm of quantum mechanics. We explore various types of quantum entropy, including von Neumann entropy, relative entropy, and a newly proposed generalized entropy, denoted as *Eg*. The definition of *Eg* is based on a novel approach that considers the entanglement structure and correlations within quantum states. We establish relationships between these different entropy measures, demonstrating their interconnectedness within the broader context of quantum information theory. The paper further outlines a mathematical formalism for calculating *Eg*, providing a tool for analyzing and characterizing quantum information. Our generalized entropy provides a more flexible and potentially more accurate measure of quantum information, particularly in scenarios involving complex quantum correlations and multi-partite quantum systems. ---

DOI: 10.5281/zenodo.22201517

Related papers

Information-Theoretic Characterization of Non-Classical Entanglement Entropy

Jincheng Zhang

This paper introduces a novel entropy concept – non-classical entanglement entropy – designed to quantify the complexity and information content of quantum entanglement states. Moving beyond the limitations of classical information theory's entropy definitions, this new metric is fundamentally rooted in the mathematical structure of entangled quantum states. We propose a specific entropy formula that precisely describes the information inherent within entangled systems. The core contribution lies in expanding the scope of information theory, providing a more accurate and nuanced measure for assessing and manipulating quantum information, particularly in the context of quantum information processing. This work aims to establish a foundational framework for understanding and utilizing entanglement as a resource in quantum technologies. ---

Aug 31, 20260 citations

Non-Classical Information Entropy: A Statistical Physics Perspective

Jincheng Zhang

This paper introduces a novel definition of non-classical information entropy, rooted in the principles of statistical physics, particularly quantum mechanics. The core premise is that traditional information entropy, derived from classical probability theory, is insufficient to capture the essence of information within non-classical systems exhibiting phenomena such as superposition and entanglement. We propose a definition based on the concept of accessible states and their associated probabilities, extending the notion of entropy beyond the realm of purely deterministic systems. The paper details the mathematical formulation of this non-classical information entropy, denoted as *Hnc*, and presents a method for its calculation. The method relies on identifying the set of accessible states for a given system and then applying a generalized form of Shannon's entropy formula, modified to account for the inherent uncertainties associated with quantum mechanics. The resulting *Hnc* provides a quantitative measure of the information content within non-classical systems, offering a potential framework for studying information processing and dynamics in quantum environments. The key contribution lies in bridging the gap between information theory and non-classical statistical physics, offering a new lens through which to understand information in quantum systems.

Sep 3, 20260 citations

Quantum Entanglement Entropy Information Theory

Jincheng Zhang

This paper introduces a novel approach to information theory, leveraging quantum entanglement entropy as a fundamental measure of information. We propose that entanglement entropy can effectively quantify the efficiency of information transmission and provides a theoretical foundation that surpasses the limitations of classical information theory. The core of this work lies in the integration of entanglement entropy with Shannon entropy, establishing a new framework for analyzing information transfer. We explore scenarios where classical information theory struggles to adequately describe the limits of communication due to quantum mechanical effects, specifically entanglement. The paper aims to provide a theoretical underpinning for quantum communication protocols and potentially inform the development of quantum computation. We define key terms and formulate core concepts, focusing on the relationship between entanglement entropy, information content, and the constraints imposed by quantum mechanics. The central argument is that by considering the inherent interconnectedness of entangled systems, we can gain a deeper understanding of information processing at the most fundamental level. ---

Sep 3, 20260 citations

Quantum Entanglement Entropy: A Novel Metric for Quantifying Entanglement

Jincheng Zhang

This paper introduces a novel approach to quantifying quantum entanglement using entanglement entropy. Traditional entanglement measures, such as concurrence and entanglement of formation, often struggle to fully capture the intricate correlations present in entangled states. We propose a new definition of entanglement entropy based on the density matrix of the entangled system, explicitly accounting for the correlations between subsystems. This approach leverages information-theoretic entropy calculations to provide a more precise and comprehensive measure of entanglement strength and the degree of correlation. We demonstrate that this entropy-based metric offers advantages over existing measures, particularly in characterizing complex entangled states and distinguishing between different levels of entanglement. The core claim is that entanglement entropy can serve as a more accurate indicator of entanglement than existing metrics. The underlying mechanism centers around a density matrix-based entropy calculation, recognizing the interconnectedness within entangled states. The novelty lies in moving beyond purely state-based descriptions to incorporate a measure of subsystem correlations.

Aug 28, 20260 citations

Quantum logical entropy: fundamentals and general properties

Boaz Tamir, Ismael L. Paiva, Zohar Schwartzman-Nowik +1 more

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

arXiv:2108.027264openJan 1, 20228 citations

Quantum Entanglement Information Entropy Precise Calculation

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, exhibits a unique and profoundly complex information structure. Measuring entangled particles simultaneously reveals correlations that defy classical intuition. This paper explores a novel approach to precisely quantify this entanglement information entropy, presenting a method based on the calculated value of the entanglement entropy. We propose a new algorithm designed to accurately represent and quantify the intricate correlations present in entangled systems, with implications for advancing quantum communication and computation. The core mechanism centers around leveraging the inherent statistical properties of entanglement, aiming to surpass current methods in providing a robust and accurate representation of the entangled state. This research will focus on demonstrating the algorithm's capabilities through rigorous mathematical derivations and illustrative examples.

Sep 7, 20260 citations