Monogamy and polygamy relations of multiqubit entanglement based on unified entropy*

Abstract

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.

Unified entropy entanglement with tighter constraints on multipartite systems

“…On the other hand, comparing with another class of multiqubit monogamy inequalities in terms of α-th power of UE provided by Ref. [24], Theorem 2 may show its superiority. In fact, the authors in Ref.…”

“…[17] Later, tight classes of monogamy and polygamy inequalities of multiqubit entanglement using the non-negative power of various entanglement measures were also proposed, [18][19][20][21][22] and a monogamy and polygamy relations of multiqubit entanglement in terms of unified entropy were given. [23,24] In this paper, we provide a full characterization of multiqubit entanglement monogamy and polygamy constraints in terms of non-negative power of entanglement measures based on unified entropy. [25,26] We devote to completing a class of tight monogamy inequalities of multiqubit entanglement based on the α-th power of unified-(q, s) entanglement for α ≥ 1.…”

Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations

“…The red solid line represents the Tsallis-2 entanglement of assistance z0 of |ψ ABC in Example 2. The green dotted line represents the upper bound z1 from our result, and the yellow dashed line represents the upper bound z2 from[32].…”

“…Dual to the monogamy relation, the polygamy relation [31] is described by E(ρ A|BC ) ≤ E(ρ AB ) + E(ρ AC ). Polygamy relations have been similarly studied under different entanglement measures [32] for multipartite quantum systems as well as some higher-dimensional quantum systems [33][34][35].…”

Effects of colored noise on the dynamics of quantum entanglement of a one-parameter qubit–qutrit system

“…[28] Quantum entanglement has several properties including the monogamy relation, which is characterized by the distribution of entanglement in multipartite systems. [29] The relationships of monogamy and polygamy help to distribute entanglement in multipartite systems. These relationships of monogamy and polygamy are closer than those related to the i-th power of the entanglement-based measure in Renyi entropy.…”