Locally distinguishing genuinely nonlocal sets with one GHZ state

The article explores the intricate problem of quantum state discrimination, focusing on sets of orthogonal quantum states that are indistinguishable under Local Operations and Classical Communication (LOCC). It delves into the concept of genuine nonlocality, where quantum states exhibit nonlocal properties even in the absence of entanglement, a phenomenon known as 'quantum nonlocality without entanglement.' The publication constructs genuinely nonlocal product states in various multipartite systems, demonstrating how these states can be perfectly distinguished using minimal entangled resources, specifically GHZ states. The article generalizes existing constructions to higher-dimensional systems and arbitrary numbers of particles, providing a more comprehensive understanding of quantum nonlocality. It also highlights the practical applications of these findings in quantum information processing, including quantum computing, communication, and cryptography. The efficient use of entangled resources and the minimal genuine nonlocality of the constructed sets are particularly noteworthy, offering new insights and tools for advancing quantum technologies.