MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Nonlocality of orthogonal product basis quantum states

Yan-Ling Wang, Mao-Sheng Li, Zhu-Jun Zheng and Shao-Ming Fei


We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of $\mathbb{C}^d\otimes\mathbb{C}^d$, where $d$ is odd, Zhang \emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {\bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system $\mathbb{C}^m\otimes\mathbb{C}^n$. We present a small set with only $3(m+n)-9$ orthogonal product states and prove these states are LOCC indistinguishable. Even though these $3(m+n)-9$ product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.

03.67.Hk, 03.65.Ud

Related publications

2015 Repository Open Access
Yan-Ling Wang, Mao-Sheng Li, Zhu-Jun Zheng and Shao-Ming Fei

Nonlocality of orthogonal product-basis quantum states

In: Physical review / A, 92 (2015) 3, p. 032313