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

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 W-class states using Rényi-α entropy. First, we present analytical formulas of Rényi-α entanglement (RαE) and Rényi-α entanglement of assistance (RαEoA) for a reduced density matrix of an n-qudit pure state in a superposition of generalized W-class states and vacuum. Based on the analytical formulas, we show monogamy and polygamy relations in terms of RαE and RαEoA. Next a reciprocal relation of RαEoA 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 W-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.