Abstract We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.
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.
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.
Abstract Monogamy and polygamy relations quantify complementary restrictions on the distribution of entanglement in multipartite quantum systems. We establish two endpoint-matched scalar inequalities that retain a hierarchy-dependent mixed term discarded by standard weighted estimates. Conditional on a valid base-power monogamy or polygamy relation for the chosen entanglement quantity and state class, these inequalities yield refined tripartite bounds and recursive extensions to arbitrary numbers of parties. Analytical comparison with earlier coefficients proves that the resulting monogamy lower bounds are no smaller and the polygamy upper bounds are no larger throughout the common parameter domain. Concurrence and concurrence-of-assistance examples verify the ordering and identify the equality conditions.
For a bipartite entanglement measure
E that satisfies the
γth-power monogamy inequality (Eq.~\eqref{e:chap1-ineq1}), and for its assisted counterpart
Ea that obeys the
δth-power polygamy inequality (Eq.~\eqref{e:chap1-ineq2}), we introduce a unified, tunable framework indexed by a parameter
m≥1. Within this framework, we derive two hierarchical families of refined inequalities:
a tightened
α-power monogamy relation for
E, valid for all
α≥mγ;
a tightened
β-power polygamy relation for
Ea, applicable for
(m−1)δ<β≤mδ.
As
m increases, the bounds become progressively tighter, recovering known results at
m=1. Notably, the optimal monogamy bound emerges as a piecewise function of
α, with additional correction terms activated as
α crosses successive integer thresholds, thereby offering a sharper characterization of entanglement distribution.
We demonstrate that our results generalize and strengthen existing monogamy and polygamy relations through analytical comparisons and numerical evaluations using concurrence and concurrence of assistance. This hierarchical, parameterized approach offers enhanced and flexible tools for applications in quantum communication, quantum networks, and multipartite quantum information processing.