Local distinguishability of five orthogonal product states on bipartite and tripartite quantum systems
Guang-Bao Xu, Zi-Yan Hao, Hua-Kun Wang, Yu-Guang Yang, Dong-Huan Jiang
TL;DR
This work addresses the problem of local distinguishability for five orthogonal product states on bipartite and tripartite quantum systems. It introduces the vector of pairwise orthogonal relations, using it to classify five bipartite OPSs into six categories and five tripartite OPSs into eight categories, and then derives LOCC-discrimination results for each category. Most categories yield perfect LOCC distinguishability, with explicit protocols, while a finite set of exceptional graphs resist perfect discrimination or require probabilistic strategies, including quantified success probabilities. The findings advance the understanding of quantum nonlocality without entanglement and provide a structural framework (via orthogonality graphs and relation vectors) useful for analyzing local distinguishability in multipartite OPS sets.
Abstract
Local distinguishability of orthogonal quantum states can effectively reduce the consumption of quantum resources and lower economic costs in quantum protocols. Although numerous achievements have been made regarding local distinguishability of orthogonal quantum states, some fundamental issues have not been effectively addressed. For example, the local distinguishability of five orthogonal product states (OPSs) is still unknown up to now. In this paper, we give the properties of local distinguishability of five OPSs on bipartite and tripartite quantum systems. Firstly, to characterize the structure of a set of bipartite OPSs, we propose the concept of the vector of orthogonal relations for a set of bipartite OPSs. Secondly, we classify the structures of five bipartite OPSs into six categories by this concept and prove that five of these six categories can be perfectly distinguished by local operations and classical communication (LOCC). Thirdly we show that the local distinguishability of each case of the sixth category singly. On the other hand, we first divide the structures of five tripartite OPSs into eight categories by the vectors of orthogonal relations of five tripartite OPSs. Then we give the local distinguishability of each category. Our work enriches the research results of quantum nonlocality and will provide a clear understanding of the local distinguishability of five OPSs.