High-dimensional GHZ-based multi-party quantum key agreement: rigorous security, fairness, and loss tolerance

Abstract

This paper presents an efficient approach for quantum state estimation based on low-rank matrix completion. The proposed method reconstructs pure quantum states using a significantly reduced number of measurement settings while avoiding the need for experimentally challenging entangling measurements. By relying only on local measurements, the method lowers computational and experimental complexity and improves the practicality of quantum state tomography on current quantum devices. Numerical evaluations demonstrate that the proposed technique achieves high reconstruction accuracy and outperforms several existing approaches when estimating multi-qubit quantum states. The method provides an effective and scalable solution for characterizing quantum systems and can serve as a valuable tool for benchmarking and validating the performance of present and future quantum computing platforms.