# Alternative method for deriving nonlocal multipartite product states

## TL;DR

This paper introduces a new class of multipartite product states that require infinite measurement rounds for perfect local distinguishability, expanding understanding of nonlocality without entanglement.

## Contribution

It proposes a novel method for constructing LOCC indistinguishable states by appending nonorthogonal states, differing from previous approaches.

## Key findings

- States require infinite rounds of LOCC to distinguish
- Appended states remain LOCC indistinguishable
- Some parties can perform nontrivial measurements

## Abstract

We can only perform a finite rounds of measurements in protocols with local operations and classical communication (LOCC). In this paper, we propose a set of product states, which require infinite rounds of measurements in order to distinguish this given set of states perfectly by LOCC. Therefore, we can conclude that these sets of states are locally indistinguishable. More accurately, given any multipartite LOCC indistinguishable set where every local system cannot start with a nontrivial measurement, then after appending these states with arbitrarily choosing two nonorthogonal states, we obtain another LOCC indistinguishable set. It can be seen that some parties can perform some nontrivial measurements. Hence, these sets are quite different from those constructed before. This result broadens the knowledge of nonlocality without entanglement to a certain extent.