Complementary monogamy and polygamy properties among multipartite systems

Monogamy and polygamy relations are essential properties of quantum entanglement,which characterize the distributions of entanglement in multipartite systems.In this paper,we establish the general monogamy relations forγ-th(0≤γ≤α,α≥1)power of quantum entanglement based on unified-(q,s)entanglement and polygamy relations forδ-th(δ≥β,0≤β≤1)power of entanglement of assistance based on unified-(q,s)entanglement of assistance,which provides a complement to the previous research in terms of different parameter regions ofγandδ.These results are then applied to specific quantum correlations,e.g.,entanglement of formation,Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities.Moreover,typical examples are presented for illustration.

Parameterized monogamy and polygamy relations of multipartite entanglement

Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence（SC） and square of quantum discord（SQD）. The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Monogamy and polygamy relations of multiqubit entanglement based on unified entropy

Monogamy relation is one of the essential properties of quantum entanglement,which characterizes the distribution of entanglement in a multipartite system.By virtual of the unified-(q,s)entropy,we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures.For the multiqubit system,a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s)entanglement for α≥1.We also obtain a class of tighter polygamy relations in the β-th(0≤β≤1)power of unified-(q,s)entanglement of assistance.Applying these results to specific quantum correlations,e.g.,entanglement of formation,Renyi-q entanglement of assistance,and Tsallis-q entanglement of assistance,we obtain the corresponding monogamy and polygamy relations.Typical examples are presented for illustration.Furthermore,the complementary monogamy and polygamy relations are investigated for the α-th(0≤α≤ 1)and β-th(β≥1)powers of unified entropy,respectively,and the corresponding monogamy and polygamy inequalities are obtained.

Monogamy of quantum correlations in the one-dimensional anisotropic XXXYYY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with stag- gered Dzyaloshinskii-Moriya （DM） interaction have been investigated using the quantum renormalization group （QRG） method. We summarize the monogamy relation for different quantum correlation measures and make an explicit compar- ison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.

Monogamy relations of quantum entanglement for partially coherently superposed states

Monogamy is a fundamental property of multi-partite entangled states. Recently, Kim J S[Phys. Rev. A 93 032331] showed that a partially coherent superposition （PCS） of a generalized W-class state and the vacuum saturates the strong monogamy inequality proposed by Regula B et al.[Phys. Rev. Lett. 113 110501] in terms of squared convex roof extended negativity; and this fact may present that this class of states are good candidates for studying the monogamy of entanglement. Hence in this paper, we will investigate the monogamy relations for the PCS states. We first present some properties of the PCS states that are useful for providing our main theorems. Then we present several monogamy inequalities for the PCS states in terms of some entanglement measures.

Monogamy relations in tripartite quantum system

This paper presents monogamy relations for three-qubit quantum states by using convex-roof extended negativity, which inspires studying the difference between the three entanglement measures, concurrence, negativity and convex- roof extended negativity. It finds that the convex-roof extended negativity is a stronger entanglement measure than concurrence in multipaxtite higher-dimensional quantum system.

Optimized monogamy and polygamy inequalities for multipartite qubit entanglement

We investigate the monogamy and polygamy inequalities of arbitrary multipartite quantum states,and provide new classes of monogamy and polygamy inequalities of multiqubit entanglement in terms o f concurrence,entanglement of formation,negativity,and Tsallis-q entanglement,respectively.We show that these new monogamy and polygamy inequality relations are tighter than the existing ones with detailed examples.

What Does Monogamy in Higher Powers of a Correlation Measure Mean?

We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality needs not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.

Monogamy and polygamy for the generalized W-class states using unified-(q,s)entropy

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q,s)entropy.Firstly,we provide an analytical formula of unified-(q,s)entanglement(UE)and an analytical lower bound of unified-(q,s)entanglement of assistance(UEo A)for a reduced density matrix of a generalized W-class state.Then,we use these two analytical formulas to derive the monogamy and polygamy inequalities for a reduced density matrix of a qudit generalized W-class(GW)state.We establish two partition-dependent residual entanglements based on the new monogamy relation,which is helpful to obtain a comprehensive analysis of entanglement dynamics of generalized W-class states.Further,we investigate tighter monogamy and polygamy relations based on the power ofαth(α≥0)for UE andβth(β≥0)for UEo A,respectively.The results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.

Monogamy of Measurement-Induced Nonlocality Based on Relative Entropy

In this paper, using relative entropy, we study monogamous properties of measurement-induced nonlocality based on relative entropy. Depending on different measurement sides, we provide necessary and sufficient conditions for two types of monogamy inequalities. By the concept of nonlocality monogamy score, we find a necessary condition of the vanished nonlocality monogamy score for arbitrary three-party states. In addition, two types of necessary and sufficient conditions of the vanished nonlocality monogamy scores are obtained for any pure states. As an application, we show that measurement-induced nonlocality based on relative entropy can be viewed as a "nonlocality witness" to distinguish generalized GHZ states from the generalized W states.

Exhibition of Monogamy Relations between Entropic Non-contextuality Inequalities

We exhibit the monogamy relation between two entropic non-contextuality inequalities in the scenario where compatible projectors are orthogonal. We show the monogamy relation can be exhibited by decomposing the orthogonality graph into perfect induced subgraphs. Then we find two entropic non-contextuality inequalities are monogamous while the KCBS-type non-contextuality inequalities are not if the orthogonality graphs of the observable sets are two odd cycles with two shared vertices.

Tighter monogamy relations of multiqubit entanglement in terms of Rényi-α entanglement

We explore the existence of monogamy relations in terms of Rényi-α entanglement. By using the power of the Rényi-α entanglement, we establish a class of tight monogamy relations of multiqubit entanglement with larger lower bounds than the existing monogamy relations for α≥2, the power η>1, and 2>α≥(71/2-1)/2, the power η>2, respectively.

Unified entropy entanglement with tighter constraints on multipartite systems

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide a characterization of multiqubit entanglement constraints in terms of unified-(q,s)entropy.A class of tighter monogamy inequalities of multiqubit entanglement based on theα-th power of unified-(q,s)entanglement forα≥1 and a class of polygamy inequalities in terms of theβ-th power of unified-(q,s)entanglement of assistance are established in this paper.Our results present a general class of the monogamy and polygamy relations for bipartite entanglement measures based on unified-(q,s)entropy,which are tighter than the existing ones.What is more,some usual monogamy and polygamy relations,such as monogamy and polygamy relations based on entanglement of formation,Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance,can be obtained from these results by choosing appropriate parameters(q,s)in unified-(q,s)entropy entanglement.Typical examples are also presented for illustration.

Mental health and polygamy: The Syrian case

AIM: To examine the psychological, self-esteem(SE), family function, marital satisfaction, life satisfaction and degree of agreement with the practice of polygamy among polygamous women with a control group from monogamous women in Syria. METHODS: Convenience sample of 136 women, 64 of whom were wives in polygamous marriages and 72 were wives in monogamous marriages participated in this study. A snowball method of sampling was used, conducted by undergraduate local female students trained to collect data according to culturally competent methods. The following research instruments were deployed: the symptoms checklist-90, the Rosenberg SE, the Life Satisfaction, family function and marital satisfaction. RESULTS: Findings revealed that women in polygamous marriages experienced lower SE, less life satisfaction, less marital satisfaction and more mental health symptomatology than women in monogamous marriages. Many of the mental health symptoms were different; noteworthy were elevated somatization, depression, hostility and psychoticism and their general severity index was higher. Furthermore, "first wife syndrome" was examined in polygamous families, comparing first with second and third wives in polygamous marriages. Findings indicated that first wives reported on more family problems, less SE, more anxiety, moreparanoid ideation, and more psychoticism than second and third wives. CONCLUSION: These results are best understood through consideration of the socio-cultural and economic realities facing these women. Implications for mental health practice, policy and further research are discussed.

Measurement-induced nonlocality in the W and Greenberger–Horne–Zeilinger superposition states

Measurement-induced nonlocality（MIN） is a newly defined quantity to measure correlations in bipartite quantum states [Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401]. MIN in the n-qubit W and Greenberger–Horne–Zeilinger（GHZ） superposition states is considered. It is revealed that n = 3 and n ≥ 4 states have very different characteristics,especially the monogamy relation about MIN, and the monogamy equality of MIN is held in all n-qubit W states（n ≥ 3）.

Tighter constraints of multiqubit entanglement in terms of Renyi-α entropy

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 theµ-th power of the entanglement measure based on Renyi-αentropy,as well as polygamy relations in terms of theµ-th power of Renyi-αentanglement of assistance.These monogamy and polygamy relations are shown to be tighter than the existing ones.

Monogamous nature of symmetric N-qubit states of the W class: Concurrence and negativity tangle

Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W class of states is shown to be non-zero, illustrating the fact that the concurrence tangle is always lesser than or equal to the negativity tangle in a pure N-qubit state.

Tighter Constraints of Multiqubit Entanglement

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.

Physical separation from the mate diminishes male＇s attentiveness towards other females： a study in monogamous prairie voles Microtus ochrogaster

We tested whether continuous cohabitation in monogamous voles affects the mated male＇s atten-tiveness to his breeding partner versus another female. Each male was housed in a 3-chamber ap-paratus with a Focal female （FF） and a Control female （CF） for 13 days then placed in a T-maze toassess his attentiveness to and memory of those females. The Distal male remained physically sep-arated from both females, but received their distal cues. The Separate male cohabited with the FFfor 3 days then remained physically separated from both females. The Disrupt male＇s continuouscohabitation with the FF was disrupted by having him physically separated from her after 10 daysand placed with the CF for the last 3 days. The Continuous male cohabited continuously with the FFfor 13 days. With females in the T-maze, the Separate and Disrupt males spent more time near theFF＇s box and the Disrupt males spent more time manipulating the FF＇s box than the CF＇s box. TheSeparate males groomed themselves more when near the FF＇s box than the CF＇s box. The Distaland Continuous males＇ attentiveness to the two females did not differ. Results suggest that phys-ical distance from the partner may reduce male＇s attentiveness toward other potential mates.Prairie voles might be similar to socially monogamous primates in using tactile cues as a signal formaintaining their social bonds.