Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$\alpha$ entropy

Abstract

We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$\alpha$ entropy. First, we present an analytical formula on Rényi-$\alpha$ entanglement (R$\alpha$E) and Rényi-$\alpha$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$\alpha$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$\alpha$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$\alpha$E by the analytical expression between R$\alpha$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.

arXiv comment17 pages, 3 figures

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Cited by in corpus (7)

• Monogamy of quantum entanglement
• Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum
• Multipartite entanglement measures based on the thermodynamic framework
• W-class states-identification and quantification of Bell-CHSH inequalities' violation
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• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• Monogamy of entanglement of maximal dimension