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arXiv:2109.11272 · Journal of Physics A Mathematical and Theoretical

Tighter monogamy and polygamy relations for a superposition of the generalized W -class state and vacuum

Le-Min Lai, Shao-Ming Fei, Zhi-Xi Wang

Published Sep 7, 2021• 6 citations
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Abstract

Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized W -class state and vacuum in terms of the Tsallis- q entanglement and the Rényi- α entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.

DOI
10.1088/1751-8121/ac2475

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Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized W -class state and vacuum in terms of the Tsallis- q entanglement and the Rényi- α entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.
Entanglement monogamy and polygamy are indispensable features of multipartite quantum systems that describe the entanglement distribution characteristics in these systems. Under the arbitrary partition of superposition of generalized W-class and vacuum states, we investigate a class of monogamy and polygamy inequality based on Tsallis-q and Rényi-q entropy entanglements. We show with concrete examples that parameter selection reduces these inequalities to some existing inequalities; that is, the existing inequalities can be considered a special case of this new class of inequality. Otherwise, these inequalities are tighter than existing ones and are finer representations of entanglement distributions in tripartite and multipartite quantum systems. The inequality of monogamy and polygamy established in this paper has wider applicability.
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 WWW-class states using R\'enyi-$\ensuremath{\alpha}$ entropy. First, we present analytical formulas of R\'enyi-$\ensuremath{\alpha}$ entanglement $(\mathrm{R}\ensuremath{\alpha}\mathrm{E})$ and R\'enyi-$\ensuremath{\alpha}$ entanglement of assistance $(\mathrm{R}\ensuremath{\alpha}\mathrm{EoA})$ for a reduced density matrix of an nnn-qudit pure state in a superposition of generalized WWW-class states and vacuum. Based on the analytical formulas, we show monogamy and polygamy relations in terms of $\mathrm{R}\ensuremath{\alpha}\mathrm{E}$ and $\mathrm{R}\ensuremath{\alpha}\mathrm{EoA}$. Next a reciprocal relation of $\mathrm{R}\ensuremath{\alpha}\mathrm{EoA}$ 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 WWW-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.
Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.
Abstract The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.