Title: Quantum Information Theory via Hypergeometric Distributions

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum information theory, a foundational field within quantum computing and cryptography, relies heavily on the precise manipulation and analysis of quantum states. Traditional approaches often struggle to adequately represent and quantify the complexities inherent in these states. This paper proposes a novel framework based on hypergeometric distributions to formalize the mathematical foundations of quantum information theory, offering a rigorous and powerful tool for predicting and analyzing quantum phenomena. Hypergeometric distributions, a specialized distribution in probability theory, provide a natural and efficient way to model the correlated nature of quantum states, leading to a more robust and adaptable mathematical foundation. The core mechanism involves developing new mathematical tools to quantify fidelity and entanglement, thereby facilitating the design of quantum algorithms. This work aims to bridge the gap between theoretical concepts and practical applications, potentially unlocking new algorithmic possibilities and pushing the boundaries of quantum information processing.

DOI: 10.5281/zenodo.22187541

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