2024/08/06 by Li, Hong-Run, Zuo, Hui-Juan, Shi, Fei +1
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2408.02894
Quantum nonlocality based on state discrimination describes the global property of the set of orthogonal states and has a wide range of applications in quantum cryptographic protocols. Strongest nonlocality is the strongest form of quantum nonlocality recently presented in multipartite quantum systems: a set of orthogonal multipartite quantum states is strongest nonlocal if the only orthogonality-preserving local measurements on the subsystems in every bipartition are trivial. In this work, we found a construction of strongest nonlocal sets in ℂ^d1⊗ ℂ^d2⊗ ℂ^d3 (2≤ d1≤ d2≤ d3) of size d2d3+1 without stopper states. Then we obtain the strongest nonlocal sets in four-partite systems with d3+1 orthogonal states in ℂd⊗ ℂd⊗ ℂd⊗ ℂd (d≥2) and d2d3d4+1 orthogonal states in ℂ^d1⊗ ℂ^d2⊗ ℂ^d3⊗ ℂ^d4 (2≤ d1≤ d2≤ d3≤ d4). Surprisingly, the number of the elements in all above constructions perfectly reaches the recent conjectured lower bound and reduces the size of the strongest nonlocal set in ℂd⊗ ℂd⊗ ℂd⊗ ℂd of [\hrefhttps://doi.org/10.1103/PhysRevA.108.062407Phys. Rev. A 108, 062407 (2023)] by d-2. In particular, the general optimal construction of the strongest nonlocal set in four-partite system is completely solved for the first time, which further highlights the theory of quantum nonlocality from the perspective of state discrimination.