Title: Quantum Information Theory and Geometric Probability

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Quantum Information Theory (QIT) represents a burgeoning field exploring the potential of quantum mechanics to revolutionize computation and communication. A core challenge lies in defining and manipulating probability, traditionally viewed as a statistical concept. This paper proposes a fundamental shift in perspective, formalizing "geometric probability" as a property inherent to quantum systems, and subsequently utilizing this concept to drive the development of novel quantum algorithms. The core claim centers on the idea that geometric probability offers a more direct and powerful pathway to understanding and exploiting quantum phenomena. We investigate the extension of probability to the space of geometric configurations, introducing a new type of probability intrinsically linked to quantum mechanics. This approach moves beyond traditional statistical interpretations, offering a deeper and more mathematically rigorous foundation for quantum information processing. The proposed framework necessitates a re-evaluation of fundamental probability principles, with the potential for significant advancements in algorithm design and the exploration of novel quantum computational paradigms. This work addresses the limitations of current approaches by introducing a geometric perspective that directly reflects the underlying structure of quantum mechanics.

DOI: 10.5281/zenodo.22598912

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