Journal of Quantum Cryptography | Volume 1, Issue 1: 35-54, 2025 | DOI: 10.62762/JQC.2026.133798
Abstract
Mixed quantum states exhibit a rich geometric structure from the information geometry of density operators and their purifications. Parallel transport via the Uhlmann connection induces holonomy transformations along closed trajectories of density operators. Although extensively studied in quantum physics, their potential as information-theoretic resources in quantum cryptography remains largely unexplored. This work investigates whether holonomy in the purification bundle can serve as a secrecy resource for mixed-state quantum systems. The key observation is that while a density-operator trajectory describes only the base manifold, the lifted trajectory depends on an additional unitary gaug... More >
Graphical Abstract