# Distinguishability classes, resource sharing, and bound entanglement distribution

## TL;DR

This paper classifies multipartite product states based on their distinguishability by LOCC in various partitions, explores resource sharing for LOCC indistinguishability, and presents a protocol to distribute bound entanglement using separable states.

## Contribution

It introduces a classification scheme for multipartite product states based on LOCC distinguishability and proposes a protocol for distributing bound entanglement using separable states.

## Key findings

- Classification of tripartite and multipartite product states based on LOCC distinguishability.
- Identification of resource sharing strategies for LOCC indistinguishable sets.
- Protocol for distributing bound entanglement using separable states.

## Abstract

Suppose a set of $m$-partite, $m\geq3$, pure orthogonal fully separable states is given. We consider the task of distinguishing these states perfectly by local operations and classical communication (LOCC) in different $k$-partitions, $1<k<m$. Based on this task, it is possible to classify the sets of product states into different classes. For tripartite systems, a classification of the sets with explicit examples is presented. Few important cases related to the aforesaid task are also studied when the number of parties, $m\geq4$. These cases never appear for a tripartite system. However, to distinguish any LOCC indistinguishable set, entanglement can be used as resource. An important objective of the present study is to learn about the efficient ways of resource sharing among the parties. We also find an interesting application of multipartite product states which are LOCC indistinguishable in a particular $k$-partition. Starting from such product states, we constitute a protocol to distribute bound entanglement between two spatially separated parties by sending a separable qubit.