Superactivation of monogamy relations for nonadditive quantum correlation measures

We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\alpha$ and $\beta$ such that for any quantum correlation measure $Q$, $Q^x$ is monogamous if $x\geq \alpha$ and polygamous if $0\leq x\leq \beta$ for a given multipartite state $\rho$. For $\beta <x<\alpha$, we show that the monogamy relation can be superactivated by finite $m$ copies $\rho^{\otimes m}$ of $\rho$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last

General polygamy inequality of multi-party quantum entanglement

Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.Comment: 4 pages, 1 figur

Strong polygamy of quantum correlations in multi-party quantum systems

We propose a new type of polygamy inequality for multi-party quantum entanglement. We first consider the possible amount of bipartite entanglement distributed between a fixed party and any subset of the rest parties in a multi-party quantum system. By using the summation of these distributed entanglements, we provide an upper bound of the distributed entanglement between a party and the rest in multi-party quantum systems. We then show that this upper bound also plays as a lower bound of the usual polygamy inequality, therefore the strong polygamy of multi-party quantum entanglement. For the case of multi-party pure states, we further show that the strong polygamy of entanglement implies the strong polygamy of quantum discord.Comment: 5 page

Polygamy relation of quantum correlations with equality

We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, we present polygamy inequalities satisfied by the $\beta$th $(\beta>0)$ power of the quantum correlation measures. Taking concurrence of assistance as an example, we further illustrate the significance and advantages of these relations. We also obtain a polygamy relation with equality by considering the one-to-group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. We demonstrate that such relations for tripartite states can be generalized to multipartite systems

Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy

Using R\'enyi-$\alpha$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $\alpha \geq 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-\epsilon \leq \alpha \leq 1.43+\epsilon$ with $0<\epsilon<0.01$.Comment: 19 pages, 2 figure

Polygamy relations of multipartite systems

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $\alpha$th $(\alpha\geq 2)$ power of concurrence of assistance, $\beta$th $(\beta \geq1)$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA)