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

¹  Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China
²  Department of Computer Science, Wayne State University - Detroit, MI 48202, USA
³  Electrical Engineering and Computer Science Department, University of Michigan - Ann Arbor, MI 48109, USA
⁴  Department of Mathematics, University of California - Irvine, CA 92697-3875, USA

Corresponding author: dli@math.tsinghua.edu.cn

Received: 14 May 2009
Accepted: 17 July 2009

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 l (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 excitations under SLOCC, and that all the n-qubit symmetric Dicke states with l (2 l (n-2)) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality .