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.

Entanglement and Volume Monogamy Features of Permutation Symmetric N-Qubit Pure States with N-Distinct Spinors: GHZ and States

We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.

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 a-th power of unified-(q,s) entanglement for a> 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 Tsallisq 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 theα-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 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.

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.

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.

Generated genuine tripartite steering and its monogamy in the background of a Kerr-Newman black hole

We study the redistribution of quantum steering and its monogamy in the presence of a four-dimensional Kerr-Newman black hole.The gravitational effect of the Kerr-Newman black hole is shown to generate genuine tripartite steering between causally disconnected regions,depending on the polar angle,angular momentum,electric charge,and magnetic charge of the black hole.We obtain strong evidence of steering monogamy,that is,the"sudden death"of the A→B steering results in the"sudden birth"of B→B steering.We also obtain the condition of maximal steering asymmetry,that is,η0=√1+tanh^(2)(s),revealing the transition between two-way and one-way steering in Kerr-Newman spacetime.

Monogamy Relations for Squared Entanglement Negativity

This paper contains two main contents.In the first part,we provide two counterexamples of monogamy inequalities for the squared entanglement negativity:one three-qutrit pure state which violates of the He–Vidal monogamy conjecture,and one four-qubit pure state which disproves the squared-negativity-based Regula–Martino–Lee–Adessoclass strong monogamy conjecture.In the second part,we investigate the sharing of the entanglement negativity in a composite cavity-reservoir system using the corresponding multipartite entanglement scores,and then we find that there is no simple dominating relation between multipartite entanglement scores and the entanglement negativity in composite cavity-reservoir systems.As a by-product,we further validate that the entanglement of two cavity photons is a decreasing function of the evolution time,and the entanglement will suddenly disappear interacting with independent reservoirs.

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.

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）.

Reproductive behavior in horseshoe crabs:Does density matter?

While the four species of horseshoe crabs share many common reproductive traits with respect to their reproductive systems, they do differ with respect to their mating behavior （monogamy vs. polygynandry）. Past research has attributed these differences to a number of factors including： spawning densities, operational sex ratios （OSR＇s）, male condition （or age）, environmental and/or genetic factors, or a combination thereof. Mating behaviors in the three Asian horseshoe crab species （Tachy-pleus gigas, T. tridentatus, and Carcinoscorpius rotundicauda） with low spawning densities and 1：1 operational sex ratios are typically monogamous. In Limuluspolyphemus, mating behavior is more variable ranging fi＇om monogamy to polygynandry. Here we provide evidence, through a long term behavioral study, that variation in mating behavior is influenced by population density in L. polyphemus. Our study population on two beaches in Connecticut （Long Island Sound） have a spawning density 400 times less than that found in Delaware Bay （0.002 females/m2 vs. 0.8 females/m2） but similar operational sex ratios. Between 90%-95% of all spawning females in CT were paired with only one male, thus exhibiting monogamous behavior. In contrast, between 30 and 60% of spawning females in Delaware Bay have more than one mate and produce clutches of eggs with multiple paternities. Male condition played no role in mating behavior in CT populations. We also observed that on average 18% of the females on the spawning beaches are single. These results suggest that population density is an important condition that determines mating behavior. Also, low population density may lead to decreased mate finding ability and lost opportunities for spawning

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.