Abstract
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 -class states using Rényi- entropy. First, we present analytical formulas of Rényi- entanglement and Rényi- entanglement of assistance for a reduced density matrix of an -qudit pure state in a superposition of generalized -class states and vacuum. Based on the analytical formulas, we show monogamy and polygamy relations in terms of and . Next a reciprocal relation of 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 -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.
- Received 14 May 2020
- Revised 6 December 2020
- Accepted 7 December 2020
DOI:https://doi.org/10.1103/PhysRevA.102.062428
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