Multigraphs: emergence from Hilbert space subdivision in superposed quantum systems and their image encoding application

Abstract

Quantum computing has emerged as a transformative field, offering unprecedented capabilities that promise to revolutionize various domains such as cryptography, data encoding, and information processing. This study explores the potential of quantum systems and their associated phenomena in generating pseudo-random numbers, image encryption, and multigraph representation.

Initially, this research proposes an algorithm leveraging quasi-probabilities inherent in quantum mechanics to construct a Pseudo Random Number Generator (PRNG) from a small quantum system. Through rigorous testing, the ability of this approach to generate deterministic sequences of pseudo-random numbers is demonstrated, highlighting the efficiency and unpredictability of quantum-generated random numbers.

Subsequently, an encryption and decryption algorithm based on the PRNG is developed and evaluated, analyzing its robustness against common attacks such as cropping, noise, and correlation. The findings underscore the heightened security offered by quantum-based encryption schemes, paving the way for fundamentally secure image transmission and storage.

Moreover, this research introduces a novel framework for representing multigraphs within quantum systems. This innovative approach allows the generation of graphs with varying vertex or edge label density, opening new avenues for data representation and processing.

Therefore, this study contributes to the advancement of quantum computing by demonstrating the efficacy of quantum systems in generating pseudo-random numbers, enhancing image encryption security, and offering insights into the representation of multigraphs within quantum contexts.