# Minimum quantum resources for strong non-locality

## TL;DR

This paper investigates the minimal quantum resources required to achieve strong non-locality, demonstrating that certain three-qubit states in the GHZ class with specific measurements can realize this phenomenon with finite measurements.

## Contribution

It identifies the specific class of three-qubit states capable of strong non-locality and shows an infinite family of such states with varying entanglement levels.

## Key findings

- Strong non-locality cannot be realized with two-qubit systems.
- Only GHZ SLOCC class states with equatorial measurements can realize strong non-locality.
- An infinite family of three-qubit states can realize strong non-locality with finite measurements.

## Abstract

We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non-LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreasing entanglement between one qubit and the other two, necessitating an increasing number of local measurements on the latter.