Locally distinguishing tripartite strongly nonlocal quantum states with entanglement resource.

Recently, Yuan et al. (Phys Rev A 102:042228, 2020) construct a set of strongly nonlocal orthogonal product states in C d ⊗ C d ⊗ C d , where d ≥ 3 . Then, it is interesting how much entanglement resource is sufficient to locally distinguish these states, and very little is known about entanglement-assisted distinguishing strongly nonlocal quantum states. In this paper, we first design one entanglement-assisted state discrimination protocols for strongly nonlocal orthogonal product states in C 4 ⊗ C 4 ⊗ C 4 quantum system. Then, in the same way, we give how much entanglement resource is sufficient to locally distinguish these strongly nonlocal orthogonal product states in C 5 ⊗ C 5 ⊗ C 5 , C 6 ⊗ C 6 ⊗ C 6 quantum systems. Finally, we propose a conjecture that less entanglement resource than quantum teleportation can be used to locally distinguish these strongly nonlocal quantum states in C d ⊗ C d ⊗ C d , where d ≥ 3 . The above results can illustrate the important role of entanglement resource in locally distinguishing orthogonal quantum states and also reveal the phenomenon of less nonlocality with more entanglement. [ABSTRACT FROM AUTHOR]