Title: Non-Associative Algebra and the Quantum State of Systems

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper explores the application of non-associative algebra to the representation and manipulation of quantum state systems. The current mathematical landscape often falls short in adequately capturing the intricate and non-linear entanglement patterns inherent in quantum mechanics. We propose a novel algebraic structure, termed "non-associative entanglement," designed to address these limitations by providing a framework for representing and calculating entanglement with unprecedented precision. The core claim is to establish a new class of non-associative algebras capable of accurately modeling and processing complex quantum states, facilitating automated calculations of entanglement and superposition. This work will detail the mathematical foundations of this approach, showcasing its potential to revolutionize quantum state representation and computation.

DOI: 10.5281/zenodo.22189177

Related papers

Title: Non-Euclidean Geometry for Quantum Entanglement Measurement

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge for experimental verification and manipulation. Traditional measurement techniques often fail to capture the true essence of this correlated state, leading to inaccuracies and limitations. This paper explores the utilization of non-Euclidean geometry as a foundational framework for understanding and quantifying entanglement, proposing a novel metric designed to address the inherent challenges associated with measurement. The core claim is to extend the concept of non-Euclidean geometry to provide a rigorous framework for understanding and quantifying the entanglement of quantum systems, specifically focusing on the problem of measurement. This investigation will detail the introduction of a new metric, its mathematical properties, and its potential for revolutionizing entanglement measurement. The research will also delve into the implications of this approach for quantum computing and communication, highlighting the potential for a more fundamental and precise understanding of these complex phenomena.

Sep 3, 20260 citations

Title: Quantum Entanglement-Based Nonlinear System Simulation

Jincheng Zhang

Quantum entanglement, a fundamental phenomenon in quantum mechanics, offers a unique approach to simulating complex nonlinear systems. This research explores the design of a novel simulation framework leveraging quantum entanglement to achieve enhanced accuracy and efficiency in modeling these systems. We propose a system that utilizes quantum algorithms to meticulously capture the dynamics of the system, providing precise simulation and predictive capabilities. This work addresses the limitations of traditional simulation methods, particularly in handling intricate non-linear systems, and presents a fundamentally new approach to this challenging problem. The core mechanism centers on exploiting entanglement to create a more stable and accurate representation of the system's behavior. This paper outlines the design of the framework, its potential applications, and preliminary results demonstrating its efficacy in simulating specific nonlinear systems.

Sep 3, 20260 citations

Title: A Quantum Entanglement Framework for Non-Asymptotic Proof

Jincheng Zhang

This paper presents a novel framework for proving non-asymptotic theorems based on quantum entanglement. Traditional proofs often rely on complex mathematical manipulations and lengthy calculations, limiting their applicability and efficiency. We propose a method leveraging the inherent properties of quantum entanglement to establish a rigorous and precise proof process. The core mechanism involves constructing a quantum entanglement network to represent a geometric transformation, enabling precise measurement and the establishment of the theorem's validity. This approach offers a potentially more efficient and elegant solution compared to traditional methods, reducing reliance on complex calculations and providing a robust foundation for advanced mathematical proofs. The paper details the framework's design, mathematical foundations, and preliminary experimental validation, highlighting its potential to revolutionize the field of mathematical proofs.

Sep 6, 20260 citations

Title: Non-Euclidean Geometry as a Framework for Quantum Entanglement

Jincheng Zhang

Quantum entanglement, a phenomenon where two or more particles become linked in such a way that they share the same fate no matter how far apart they are, remains a cornerstone of quantum mechanics. However, standard interpretations often struggle to fully capture its paradoxical nature and the complexities of its measurement. This paper investigates the potential of non-Euclidean geometry as a novel framework for understanding and manipulating entanglement, proposing a geometric representation that explicitly incorporates the 'non-Euclidean' property. We aim to move beyond traditional interpretations by providing a mathematically rigorous foundation for exploring entanglement's properties and offering a pathway towards novel quantum information processing techniques. This investigation centers on the hypothesis that entanglement's correlations are inherently linked to the underlying geometric structure, and that non-Euclidean geometry offers a more profound and nuanced understanding of this connection. The paper explores the conceptual implications of this framework, detailing the mathematical constructs that would be necessary to represent and manipulate entangled states within this context. We will discuss the potential benefits of this approach, including a potential resolution to the measurement problem and a deeper understanding of quantum phenomena.

Aug 31, 20260 citations

Title: Adaptive Nonlinear Geometric Transformations for Quantum Entanglement Computation

Jincheng Zhang

Quantum entanglement offers a fundamentally powerful approach to computation, surpassing the limitations of classical algorithms in certain complex scenarios. This research explores the potential of utilizing adaptive nonlinear geometric transformations to enhance quantum entanglement computation. We propose a novel framework that leverages the unique properties of entanglement to achieve precise calculations of intricate geometric transformations. The core mechanism centers around dynamically adjusting geometric parameters to optimize the entanglement's state, thereby improving the accuracy and efficiency of the computation. This work addresses the challenges of traditional computational methods with complex geometric manipulations, presenting a new perspective on quantum entanglement applications. The design introduces a sophisticated algorithm that intelligently manipulates geometric contexts to minimize errors and maximize entanglement fidelity. This approach promises to significantly advance the capabilities of quantum computation, particularly in areas involving precise geometric manipulation. The investigation of this framework is driven by the inherent strengths of entanglement and the potential for algorithmic innovation. Further, this paper will present a detailed explanation of the proposed framework, outlining its mathematical foundations and experimental validation demonstrating its effectiveness.

Sep 6, 20260 citations

Title: Non-Euclidean Quantum State Collapse – Enhanced Measurement Theory

Jincheng Zhang

This paper investigates the potential for utilizing non-Euclidean geometry to significantly enhance our understanding of quantum state collapse. Current quantum mechanics, predicated on Euclidean geometry, struggles to adequately model the probabilistic nature of entanglement and the collapse of quantum states. We propose a novel mathematical framework, incorporating non-Euclidean geometry, to represent and analyze the evolution of quantum states. The core claim is that this framework will allow for a more precise description of the collapse process and provide a deeper, more accurate understanding of the underlying physics. We will explore how this approach addresses the limitations of current models and offers a pathway toward improved predictions of measurement outcomes. The paper will detail the mathematical foundations of this approach, including the representation of entangled states within a non-Euclidean space, and demonstrate the potential for enhanced predictive capabilities.

Sep 7, 20260 citations