Strong nonlocality of orthogonal entangled states and entanglement-assisted discrimination
Jia-Xin Ma, Chen‐Ming Bai, Su-Juan Zhang
Abstract In this paper, we construct strongly nonlocal orthogonal entangled sets (SNOESs) in C 4 ⊗ C 3 ⊗ C 5 and C 5 ⊗ C 4 ⊗ C 6 . To better understand SNOESs, we introduce the concept of unitary equivalence for such sets, defined via transformations under unitary matrices. For C d 1 ⊗ C d 2 ⊗ C d 3 , we show that applying arbitrary unitary operators to a known SNOES creates new SNOESs, and we demonstrate this explicitly for C 4 ⊗ C 3 ⊗ C 5 . Our results show that any orthogonal entangled set (OES) derived from an SNOES is locally irreducible under all bipartitions, thus establishing a universal criterion for the preservation of strong nonlocality under all unitary transformations. Most importantly, the proposed method for identifying equivalent SNOESs is concise and widely applicable. Furthermore, we propose an entanglement-assisted protocol for local discrimination of our results. The protocol significantly optimizes entangled resource consumption, highlighting the practical relevance of our framework for quantum information tasks reliant on strongly nonlocal state discrimination. Our results, which can be used to classify strongly nonlocal OESs in tripartite systems, advance the theory of quantum information and deepen the structural understanding of strongly nonlocal sets.
Laser Physics Letters•Dec 1, 2025•1 citation