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

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 $C_{12}^{2}+...+C_{1n}^{2}<C_{1(2...n)}^{2}<1$.