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

Monogamy relations of all quantum correlation measures for multipartite quantum systems

The monogamy relations of quantum correlation restrict the sharability of quantum correlations in multipartite quantum states. We show that all measures of quantum correlations satisfy some kind of monogamy relations for arbitrary multipartite quantum states. Moreover, by introducing residual quantum correlations, we present tighter monogamy inequalities that are better than all the existing ones. In particular, for multi-qubit pure states, we also establish new monogamous relations based on the concurrence and concurrence of assistance under the partition of the first two qubits and the remaining ones.Comment: arXiv admin note: text overlap with arXiv:1206.4029 by other author

Quantifying quantum coherence and non-classical correlation based on Hellinger distance

Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present Hellinger distance-based measure of non-classical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, and but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit trade-off relation satisfied by the quantum coherence and this non-classical correlation

Polygamy relations of multipartite entanglement beyond qubits

We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the $\alpha$th $(0\leq \alpha\leq 2)$ 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 $\beta$th ($0\leq \beta \leq 1$) 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.Comment: arXiv admin note: text overlap with arXiv:1902.0744

Finer Distribution of Quantum Correlations among Multiqubit Systems

We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the $\alpha$th ($\alpha\geq 2$) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the $\beta$th ($0\leq \beta\leq2$) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-$q$ entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented

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)

Quantifying quantum coherence based on the generalized α−z−\alpha-z-relative Reˊ\acute{e}nyi entropy

We present a family of coherence quantifiers based on the generalized $\alpha-z-$relative R$\acute{e}$nyi entropy. These quantifiers satisfy all the standard criteria for well-defined measures of coherence, and include some existing coherence measures as special cases.Comment: 9 pages, 1 figure

Tighter generalized monogamy and polygamy relations for multiqubit systems

We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence for $N$-qubit pure states under the partition $AB$ and $C_1 . . . C_{N-2}$, as well as under the partition $ABC_1$ and $C_2\cdots C_{N-2}$. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity.Comment: arXiv admin note: substantial text overlap with arXiv:1905.0161

Strong polygamy and monogamy relations for multipartite quantum systems

Monogamy and polygamy are the most striking features of the quantum world. We investigate the monogamy and polygamy relations satisfied by all quantum correlation measures for arbitrary multipartite quantum states. By introducing residual quantum correlations, analytical polygamy inequalities are presented, which are shown to be tighter than the existing ones. Then, similar to polygamy relations, we obtain strong monogamy relations that are better than all the existing ones. Typical examples are presented for illustration