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 $l$ ($2\le l\le (n-2)$) excitations are inequivalent to the 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 $l\ne n/2$ excitations under SLOCC, and that all the $n$-qubit symmetric Dicke states with $l$ ($2\le l\le (n-2)$) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality $C_{12}^2+...+C_{1n}^2<C_{1(\mathrm{2...}n)}^2<1$.

16 pages, no figues, some changes including the title

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Cited by in corpus (9)

• Quantum secret sharing based on local distinguishability
• Entanglement in the symmetric sector of $n$ qubits
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• The n-tangle of odd n qubits
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states
• Stochastic local operations and classical communication equations and classification of even $n$ qubits
• Rank-based SLOCC classification for odd n qubits