Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.
We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the
α th
(α≥2) power of concurrence of assistance,
β th
(β≥1) power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).
We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary-dimensional quantum systems. By using the $\ensuremath{\beta}\mathrm{th}$ power of entanglement of assistance for $0\ensuremath{\le}\ensuremath{\beta}\ensuremath{\le}1$ and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of weighted polygamy inequalities of multiparty entanglement in arbitrary-dimensional quantum systems. We further show that our class of weighted polygamy inequalities can even be improved to be tighter inequalities with some conditions on the assisted entanglement of bipartite subsystems.
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.