# Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination

## TL;DR

This paper classifies genuinely nonlocal product bases in quantum systems, analyzes their local distinguishability, and demonstrates protocols that utilize entanglement for improved state discrimination.

## Contribution

It introduces a new classification of genuinely nonlocal bases and explores their discrimination using entanglement, highlighting operational advantages over teleportation.

## Key findings

- Genuinely nonlocal bases are classified based on state elimination properties.
- Protocols using shared entanglement outperform teleportation schemes.
- Genuine entanglement plays a nontrivial role in local discrimination.

## Abstract

An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation based schemes our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in local state discrimination problem.