Nonlocality of tripartite orthogonal product states

TL;DR

This paper constructs specific sets of orthogonal product states in tripartite quantum systems that are locally indistinguishable, revealing nonlocality without entanglement, and shows GHZ states can distinguish these sets.

Contribution

It introduces a method to construct locally indistinguishable tripartite product states in high-dimensional systems and demonstrates GHZ states as a resource for their discrimination.

Findings

Constructed a large set of orthogonal product states that are locally indistinguishable.

Generalized the construction method to arbitrary tripartite systems.

Proved GHZ states can distinguish the constructed states.

Abstract

Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability found in bipartite quantum systems and very few are known in multipartite systems. In this work, we construct a locally indistinguishable subset in ${\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}$, $d\geq2$ that contains $18(d-1)$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems ${\mathbb{C}}^{k}\bigotimes{\mathbb{C}}^{l}\bigotimes{\mathbb{C}}^{m}$. This result enables us to understand further the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.