Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the Rényi-$α$ entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.
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.
We investigate the tight monogamy and polygamy relations of multiparty entanglement for arbitrary quantum states. By using the power of the bipartite measure of entanglement, we establish a class of tight monogamy relations of multiparty entanglement with larger lower bounds than the existing monogamy relations. We also give a class of tight polygamy relations of multiparty entanglement with smaller upper bounds than the existing polygamy relations, by using the power of the entanglement of assistance. It is shown that these new monogamy and polygamy relations are tighter than the former resul…
We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and R'enyi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and R'enyi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented.
Using Rényi-$α$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $α\geq 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-ε\leq α\leq 1.43+ε$ with $0<ε<0.01$.
We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the $α$th ($0\leqα\leq\frac{r}{2}, r\geq2$) power of concurrence for any $2\otimes2\otimes2^{n-2}$ tripartite states and generalize it to the $n$-qubit quantum states. In addition to concurrence, we show that the monogamy relations are satisfied by other quantum correlation measures such as entanglement of formation. Moreover, the polygamy inequality of the $β$th ($β\leq0$) power of concurrence and the $β$th ($β\geq s, 0\leq s…
Monogamy and Polygamy are important properties of entanglement, which characterize the entanglement distribution of multipartite systems. We study general monogamy and polygamy relations based on the $α$th $(0\leqα\leq γ)$ power of entanglement measures and the $β$th $(β\geq δ)$ power of assisted entanglement measures, respectively. We illustrate that these monogamy and polygamy relations are tighter than the inequalities in the article [Quantum Inf Process 19, 101], so that the entanglement distribution can be more precisely described for entanglement states that satisfy stronger constraints.…
We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $α$th ($0\leqα\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polyg…
We investigate the generalized monogamy and polygamy relations $N$-qubit systems. We give a general upper bound of the $α$th ($0\leqα\leq2$) power of concurrence for $N$-qubit states. The monogamy relations satisfied by the $α$th ($0\leqα\leq2$) power of concurrence are presented 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 negativi…
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 $α$th ($0\leqα\leq2$) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the $α$th ($0\leqα\leq2$) 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…
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.
A particularly interesting feature of nonrelativistic quantum mechanics is the monogamy laws of entanglement. Although the monogamy relation has been explored extensively in the last decade, it is still not clear to what extent a given entanglement measure is monogamous. We give here a conjecture on the amount of entanglement contained in the reduced states by observing all the known related results at first. Consequently, we propose the monogamy power of an entanglement measure and the polygamy power for its dual quantity, the assisted entanglement, and show that both the monogamy power and t…
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. General monogamy relations are presented for the $α$th $(0\leqα\leqγ, γ\geq2)$ power of quantum correlation, and general polygamy relations are given for the $β$th $(β\geq δ, 0\leqδ\leq1)$ power of quantum correlation. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of $α$ and $β$. Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which…
Monogamy and polygamy relations characterize the quantum correlation distributions among multipartite quantum systems. We investigate the monogamy and polygamy relations satisfied by measures of general quantum correlation. By using the Hamming weight, we derive new monogamy and polygamy inequalities satisfied by the $β$-th power and the $α$-th power of general quantum correlations, respectively. We show that these monogamy and polygamy relations are tighter than the existing ones, such as [Int. J. Theor. Phys. 60, 1455-1470 (2021)]. Taking concurrence and the Tsallis-$q$ entanglement of assis…
We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the $β$th ($0\leqβ\leq1$) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)].
Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the $μ$th power of the entanglement measure based on Rényi-$α$ entropy, as well as polygamy relations in terms of the $μ$th powered of Rényi-$α$ entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones.
We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.
We provide a characterization of multiqubit entanglement monogamy and polygamy constraints in terms of negativity. Using the square of convex-roof extended negativity (SCREN) and the Hamming weight of the binary vector related to the distribution of subsystems proposed in Kim (Phys Rev A 97: 012334, 2018), we provide a new class of monogamy inequalities of multiqubit entanglement based on the $α$th power of SCREN for $α\geq1$ and polygamy inequalities for $0\leqα\leq1$ in terms of squared convex-roof extended negativity of assistance (SCRENoA). For the case $α<0$, we give the corresponding pol…
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-$q$ entanglement and Rényi-$α$ entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.
Entanglement polygamy, like entanglement monogamy, is a fundamental property of multipartite quantum states. We investigate the polygamy relations related to the concurrence $C$ and the entanglement of formation $E$ for general $n$-qubit states. We extend the results in [Phys. Rev. A 90, 024304 (2014)] from the parameter region $α\leq0$ to $α\leqα_0$, where $0<α_0\leq2$ for $C$, and $0<α_0\leq\sqrt{2}$ for $E$.
We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the $α$th $(0\leq α\leq 2)$ 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…
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities for the concurrence of assistance, which are shown to be tighter than the existing ones. Furthermore, analytical monogamy inequalities are obtained for the negativity of assistance.
We present classes of monogamy inequalities related to the $α$-th ($α\geq 1$) power of the entanglement measure based on the unified-($q,s$) entropy, and polygamy inequalities related to the $β$-th ($0 \leq β\leq 1$) power of the unified-($q,s$) entanglement of assistance by using Hamming weight. We show that these monogamy and polygamy inequalities are tighter than the existing ones. Detailed examples are given for illustrating the advantages.
One of the fundamental traits of quantum entanglement is the restricted shareability among multipartite quantum systems, namely monogamy of entanglement, while it is well known that monogamy inequalities are always satisfied by entanglement measures with convexity. Here we present a measure of entanglement, logarithmic convex-roof extended negativity (LCREN) satisfying important characteristics of an entanglement measure, and investigate the monogamy relation for logarithmic negativity and LCREN both without convexity. We show exactly that the $α$th power of logarithmic negativity, and a newly…
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C, the entanglement of formation E, negativity Nc and Tsallis-q entanglement Tq. Monogamy relations for the $α$th power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.
For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in …
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 $α$th ($α\geq 2$) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the $β$th ($0\leq β\leq2$) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to q…
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence $C$ and the entanglement of formation $E$. We present new entanglement monogamy relations satisfied by the $α$-th power of concurrence for all $α\geq2$, and the $α$-th power of the entanglement of formation for all $α\geq\sqrt{2}$. These monogamy relations are shown to be tighter than the existing ones.
We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates.
\indent In this article, we consider the monogamy relations for the generalized W class states. Here we first present an analytical formula on Tsallis-$q$ entanglement and Tsallis-$q$ entanglement of assistance of a reduced density matrix of the generalized W class states, then we present a monogamy relation in terms of the T$q$EE for the GW state, and we also present generalized monogamy relations in terms of T$q$EE for the GW states. At last, we present tighter polygamy relations in terms of T$q$EEoA when $q=2$ for the GWV states.
We present a class of tight monogamy relations in terms of Rényi-$α$ entanglement, which are tighter than the monogamy relations of multiqubit entanglement just based on the power of the Rényi-$α$ entanglement for $α\geq 2$ and the power $η>1$. For $2>α\geq\frac{\sqrt{7}-1}{2}$ and the power $η>2$, we establish a class of tight monogamy relations of multiqubit entanglement with larger lower bounds than the existing monogamy relations of multiqubit entanglement.
We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $α$ and $β$ such that for any quantum correlation measure $Q$, $Q^x$ is monogamous if $x\geq α$ and polygamous if $0\leq x\leq β$ for a given multipartite state $ρ$. For $β<x<α$, we show that the monogamy relation can be superactivated by finite $m$ copies $ρ^{\otimes m}$ of $ρ$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties.…
We establish a unified view of polygamy of multi-qubit entanglement. We first introduce a two-parameter generalization of entanglement of assistance namely unified entanglement of assistance for bipartite quantum states, and provide an analytic lowerbound in two-qubit systems. We show a broad class of polygamy inequalities of multi-qubit entanglement in terms of unified entanglement of assistance that encapsulates all known multi-qubit polygamy inequalities as special cases. We further show that this class of polygamy inequalities can be improved into tighter inequalities for three-qubit syste…
We investigate tight monogamy relations of multiparty quantum entanglement for any quantum state in this paper. First, we obtain a class of lower bounds for multiparty quantum systems which improve the previous results. Next, we establish a class of tighter monogamy relations in tripartite quantum systems by means of the new inequality. Furthermore, we generalize this relations to multiparty quantum systems. And then we prove the lower bounds we obtained are larger than the existing ones. Detailed examples are provided at last.
Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then i…
We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary dimensional quantum systems. By using the $β$th-power of entanglement of assistance for $0\leq β\leq1$ 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.
We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$α$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$α$E. Next, we provide tighter monogamy relations for generalized $W$-class states…
The Milburn dynamics of three nonresonant ultra-strongly coupled oscillators are resolved by using symplectic geometry. We look at the Milburn dynamics of virtual excitations and how they affect pairwise entanglement. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, we show that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, we analyze the effects of physical parameters on the redistribut…
Tsallis-$q$ entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for $q$ tending to 1. We first expand the range of $q$ for the analytic formula of Tsallis-\emph{q} entanglement. For $\frac{5-\sqrt{13}}{2} \leq \emph{q} \leq \frac{5+\sqrt{13}}{2}$, we prove the monogamy relation in terms of the squared Tsallis-$q$ entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-$q$ entanglement still works well even when the indicator based on the squared concurrence loses i…
We show that the polygamous nature of multi-party quantum correlations can be characterized in a {\em stronger} form based on Tsallis $q$-entropy and $q$-expectation value. By considering the amount of entanglement that can be distributed in multi-party systems, we establish a class of strong polygamy inequalities of multi-party entanglement in terms of Tsallis $q$-entropy and $q$-expectation for $q \geq 1$. Our new class of inequalities is in fact tighter than the usual polygamy inequalities of multi-party entanglement, and the tightness is explicitly illustrated by an example. Moreover, our …
We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$. This generalization encapsulates multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entropy for $1 \leq q \leq2$ or $3 \leq q \leq 4$, which also contains the multi-qubit polygamy inequality as a special case.
Monogamy relations characterize the distributions of quantum entanglement in multipartite systems. In this work, we present some tighter monogamy relations in terms of the power of the Tsallis-q and Rényi-$α$ entanglement in multipartite systems. We show that these new monogamy relations of multipartite entanglement with tighter lower bounds than the existing ones. Furthermore, three examples are given to illustrate the tightness.
In this paper, we present some monogamy relations of multiqubit quantum entanglement in terms of the βth power of concurrence, entanglement of formation and convex-roof extended negativity. These monogamy relations are proved to be tighter than the existing ones, together with detailed examples showing the tightness.
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy relations satisfied by the concurrence of assistance and the negativity of assistance for multiqubit generalized $W$-class states. Analytical monogamy inequalities are presented for both concurrence of assistance and negativity of assistance, which are shown to be tighter than the existing ones. Detailed examples have been presented.
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 remai…
In this paper, we study the $α$th power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations related to the $α$th power of negativity and the Convex- Roof Extended Negativity are obtained for N-qubit states. We also give a tighter bound of hierarchical monogamy inequality for the entanglement of formation. We find that the GHZ state and W state can be used to distinguish the $α$th power the concurrence for $0<α<2$. Furthermore, we compare concurrence with negativity in terms of monogamy property and investigate the difference between them.
