# Entanglement and Nonlocality in Diagonal Symmetric States of $N$-qubits

## TL;DR

This paper investigates entanglement and nonlocality in symmetric N-qubit states diagonal in the Dicke basis, revealing conditions for separability and identifying states that violate Bell inequalities despite being PPT.

## Contribution

It establishes that PPT is necessary and sufficient for separability in this set and identifies states that violate Bell inequalities despite being PPT, advancing understanding of symmetric quantum states.

## Key findings

- PPT is necessary and sufficient for separability in symmetric Dicke-diagonal states
- Identifies states that violate Bell inequalities while being PPT (weak Peres conjecture violation)
- Method extends analysis of entanglement and nonlocality to higher-dimensional symmetric states

## Abstract

We analyze entanglement and nonlocal properties of the convex set of symmetric $N$-qubits states which are diagonal in the Dicke basis. First, we demonstrate that within this set, positivity of partial transposition (PPT) is necessary and sufficient for separability --- which has also been reported recently in https://doi.org/10.1103/PhysRevA.94.060101 {Phys. Rev. A \textbf{94}, 060101(R) (2016)}. Further, we show which states among the entangled DS are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the weak Peres conjecture, being PPT with respect to one partition but violating a Bell inequality in such partition. Our method opens new directions to address entanglement and non-locality on higher dimensional symmetric states, where presently very few results are available.