Locally distinguishing nonlocal orthogonal product states with entanglement as a universal auxiliary resource

Abstract

Recently, three classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n(m\ge 3, n\ge 3)\) which cannot be exactly discriminated by local operations and classical communication (LOCC) have been constructed, respectively, by Xu et al. (Quantum Inf. Process. 20: 128, 2021) and Zhu et al. (Physica A 624: 128956, 2023). However, it is interesting to know, in order to perfectly distinguish these states by LOCC, how much entanglement resources are sufficient and/or necessary and whether it is possible to find a universal auxiliary resource. In this paper, we present that by using only one two-qubit maximally entangled state as a general auxiliary resource, the above locally indistinguishable states can all be perfectly identified by LOCC. And the general process of auxiliary local discrimination using entanglement is discussed in detail. The local distinguishing protocols we designed not only utilize minimal amount of assisted entanglement, but also show that the strength of these nonlocal sets is minimal from the point of view of auxiliary resources.