Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states

TL;DR

This paper investigates the properties of n-qubit symmetric Dicke states, demonstrating their inequivalence to GHZ and W states under SLOCC, and analyzing their monogamy relations, with implications for quantum state classification.

Contribution

It establishes the inequivalence of symmetric Dicke states to GHZ and W states under SLOCC and explores their monogamy inequalities, advancing understanding of their quantum correlations.

Findings

Dicke states with different excitations are SLOCC-inequivalent to GHZ and W states.

Even n-qubit Dicke states with n/2 excitations are inequivalent to other Dicke states with different excitations.

All Dicke states with 2≤l≤n−2 excitations satisfy generalized monogamy inequalities.

Abstract

Recently, several schemes for the experimental creation of Dicke states were described. In this paper, we show that all the $n$-qubit symmetric Dicke states with $l$ ($2\leq l\leq (n-2)$) excitations are inequivalent to the $% |GHZ>$ state or the $|W>$ state under SLOCC, that the even $n$% -qubit symmetric Dicke state with $n/2$ excitations is inequivalent to any even $n$-qubit symmetric Dicke state with $l\neq n/2$ excitations under SLOCC, and that all the $n$-qubit symmetric Dicke states with $l$ ($2\leq l\leq (n-2)$) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality $C_{12}^{2}+...+C_{1n}^{2}<C_{1(2...n)}^{2}<1$.