Monogamy and polygamy for generalized W-class states using Renyi-alpha entropy

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>Monogamy of entanglement is an indispensable feature in multipartite quantum systems. In this paper we investigate monogamy and polygamy relations with respect to any partition for generalized <b>W</b>-class states using Rényi-<b>α</b> entropy. First, we present analytical formulas of Rényi-<b>α</b> entanglement (<b>RαE</b>) and Rényi-<b>α</b> entanglement of assistance (<b>RαEoA</b>) for a reduced density matrix of an n-qudit pure state in a superposition of generalized <b>W</b>-class states and vacuum. Based on the analytical formulas, we show monogamy and polygamy relations in terms of <b>RαE</b> and <b>RαEoA</b>. Next a reciprocal relation of <b>RαEoA</b> in an arbitrary three-party quantum system is found. Later, we further develop tighter monogamy relations in terms of concurrence and convex-roof extended negativity than former ones. In order to show the usefulness of our results, two partition-dependent residual entanglements are established to get a comprehensive analysis of entanglement dynamics for generalized <b>W</b>-class states. Moreover, we apply our results to an interesting quantum game and find a bound of the difference between the quantum game and the classical game.</p></div>