LOCC distinguishable orthogonal product states with least entanglement resource

Abstract

In this paper, we construct $2n-1$ locally indistinguishable orthogonal product states in ${\mathbb{C}}^n\otimes {\mathbb{C}}^4(n>4)$ and ${\mathbb{C}}^n\otimes {\mathbb{C}}^5(n\ge 5)$ respectively. Moreover, a set of locally indistinguishable orthogonal product states with $2(n+2l)-8$ elements in ${\mathbb{C}}^n\otimes {\mathbb{C}}^{2l}(n\ge 2l>4)$ and a class of locally indistinguishable orthogonal product states with $2(n+2k+1)-7$ elements in ${\mathbb{C}}^n\otimes {\mathbb{C}}^{2k+1}(n\ge 2k+1>5)$ are also constructed respectively. These classes of quantum states are then shown to be distinguishable by local operation and classical communication (LOCC) using a suitable ${\mathbb{C}}^2\otimes {\mathbb{C}}^2$ maximally entangled state respectively.

10 pages, 3 figures