Efficient discrimination schemes for unextendible product bases with strong quantum nonlocality

Abstract

Entanglement is a central resource in quantum information science, and it is therefore important to design local discrimination protocols that minimize entanglement cost. In this paper, we propose several entanglement-assisted discrimination schemes for the local discrimination of a representative strongly nonlocal unextendible product basis (UPB) in a \(3\otimes 3\otimes 3\) system. By exploiting the structure of the UPB and the properties of maximally entangled resources, we generalize the protocols to a family of strongly nonlocal UPBs in \(d\otimes d\otimes d\) systems. In particular, we show that these UPBs can be perfectly distinguished using two bipartite maximally entangled states, distributed between different pairs of parties, without employing quantum teleportation. We further compare the total supplied and average consumed entanglement under a clearly specified accounting convention. The results demonstrate that avoiding teleportation can reduce the required entanglement in suitable resource-allocation scenarios and clarify the operational role of low-dimensional maximally entangled resources.