Nonlocality and Entanglement for Symmetric States

TL;DR

This paper explores the relationship between nonlocality and entanglement in symmetric quantum states, using numerical and semidefinite programming techniques to classify states and analyze their nonlocal properties as the number of parties increases.

Contribution

It introduces a device-independent classification of symmetric states and analyzes their nonlocality and monogamy properties, especially for large numbers of parties, using novel numerical methods.

Findings

W and GHZ states behave differently under nonlocal inequalities.

Strict monogamy is achievable for Dicke states as the number of parties grows.

Semidefinite programming effectively classifies symmetric states based on nonlocality.

Abstract

In this paper, building on some recent progress combined with numerical techniques, we shed some new light on how the nonlocality of symmetric states is related to their entanglement properties and potential usefulness in quantum information processing. We use semidefinite programming techniques to devise a device independent classification of three four qubit states into two classes inequivalent under local unitaries and permutation of systems (LUP). We study nonlocal properties when the number of parties grows large for two important classes of symmetric states: the W states and the GHZ states, showing that they behave differently under the inequalities we consider. We also discuss the monogamy arising from the nonlocal correlations of symmetric states. We show that although monogamy in a strict sense is not guaranteed for all symmetric states, strict monogamy is achievable for all Dicke states when the number of parties goes to infinity, as shown by an inequality based on a recent work studying the nonlocality (and showing strict monogamy) of W states.