Polygamy Relations Research Articles

Tighter Bounds of Generalized Monogamy and Polygamy Relations

Tighter Bounds of Generalized Monogamy and Polygamy Relations

Tighter monogamy and polygamy relations based on the generalized W-class states

Tighter monogamy and polygamy relations based on the generalized W-class states

Complete complementarity relations for quantum correlations in neutrino oscillations with CP violation

We characterize quantum correlations encoded in a three-flavor oscillating neutrino system by taking into account CP violation. By means of the complete complementarity relations (CCR), we study the trade-off of predictability, local coherence and nonlocal correlations by using relevant parameters given by neutrino oscillation experiments. Although the CCR describe very well the contributions associated to bipartite correlations, we explore the possible presence of genuine tripartite correlations, by exploiting polygamy relations. We also provide some observations about the nonlocal advantage of quantum coherence, a mazy quantum correlation characterizing the most valuable, nonlocal, portion of quantum coherence in a multi-partite system.

Weighted monogamy and polygamy relations

This research offers a comprehensive approach to strengthening both monogamous and polygamous relationships within the context of quantum correlations in multipartite quantum systems. We present the most stringent bounds for both monogamy and polygamy in multipartite systems compared to recently established relations. We show that whenever a bound is given (named it monogamy or polygamy), our bound indexed by some parameter s will always be stronger than the given bound. The study includes detailed examples, highlighting that our findings exhibit greater strength across all existing cases in comparison.

Explainable machine learning for modeling predictors of unintended pregnancy among married/in-union women in sub-Saharan Africa, a multi-country analysis of MICS 6 survey.

Unintended pregnancy is defined as a pregnancy that is either mistimed (wanted at a later time) or unwanted (not wanted at all). It has been a concerning issue for reproductive health and public health, with significant negative effects on the mother, child, and the public at large. It is a worldwide public health issue that can have a major impact on the health of pregnant women and newborns. The study was conducted using secondary data from IPUMS Multiple Indicator Cluster Surveys round 6. The analysis was based on a data merged from six sub-Saharan Africa countries such as Gambia, Ghana, Lesotho, Malawi, Nigeria, and Sierra Leone. A total weighted sample of 28,027married/in-union reproductive-age women was included in the study. Seven machine learning algorithms were trained and their performance compared in predicting unintended pregnancy. Finally, Shapley Additive exPlanations model explanation technique was used to identify the predictors of unintended pregnancy. XGBoost was the top-performing model, achieved the highest area under receiver operating characteristic curve (0.62) and accuracy (65.92%), surpassing all other models. SHAP global feature importance identified top predictors of unintended pregnancy, with women from Malawi, Ghana, and Lesotho, women having primary education and secondary education, with parity of more than three, have higher likelihood of unintended pregnancy. In the other hand, women from Nigeria and Sierra Leone, whose husband/partner has more wives or partners (polygamy relation), and women who owns mobile phone had lower risk of unintended pregnancy. These findings highlight the importance of considering contextual factors, such as country-specific sociocultural norms and individual characteristics, in understanding and addressing unintended pregnancies. By strategically addressing the identified predictors, policymakers, and healthcare providers can develop impactful programs that address the root causes of unintended pregnancies, ultimately contributing to improved reproductive health outcomes worldwide.

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 for γ-th (0 ≤ γ ≤ α, α ≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-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 of γ and δ. 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.

General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems

General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems

Polygamy Relation of Quantum Correlations with Equality

AbstractThis study provides 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, it presents polygamy inequalities satisfied by the βth power of the quantum correlation measures. Taking concurrence of assistance as an example, it further illustrates the significance and advantages of these relations. It also obtains a polygamy relation with equality by considering the one‐to‐group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. It demonstrates that such relations for tripartite states can be generalized to multipartite systems.

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.

General monogamy and polygamy properties of quantum systems

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 $$\alpha $$ th $$(0\le \alpha \le \gamma )$$ power of entanglement measures and the $$\beta $$ th $$(\beta \ge \delta )$$ power of assisted entanglement measures, respectively. We illustrate that these monogamy and polygamy relations are tighter than the inequalities in the article Jin et al. (Quantum Inf Process 19:101, 2020), so that the entanglement distribution can be more precisely described for entanglement states that satisfy stronger constraints. For specific entanglement measures such as concurrence and the convex-roof extended negativity, by applying these relations, one can yield the corresponding monogamous and polygamous inequalities, which take the existing ones in the articles Zhu and Fei (Quantum Inf Process 18:23, 2019) and Jin et al. (Quantum Inf Process 18:105, 2019) as special cases. More details are presented in the examples.

On monogamy and polygamy relations of multipartite systems

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.

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 the α-th power of unified-(q, s) entanglement for α ≥ 1 and a class of polygamy inequalities in terms of the β-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.

Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

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 $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) 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 polygamy inequalities of the $\beta$th ($\beta\geq \max\{1, s\}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.

Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations

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 $\beta$-th power and the $\alpha$-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 assistance as examples, we show the advantages of our results.

Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems

We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq2$) 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 $\beta$th ($\beta\leq0$) power of concurrence and the $\beta$th ($\beta\geq s, 0\leq s\leq1$) power of the negativity are presented for $2\otimes2\otimes2^{n-2}$. We then obtain the polygamy inequalities of quantum correlations for multipartite states. Finally, our results are shown to be tighter than previous studies using detailed examples.

Tighter Monogamy and Polygamy Relations of Quantum Entanglement in Multi-qubit Systems

We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and Rényi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and Rényi-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.

Tighter monogamy and polygamy relations for a superposition of the generalized W-class state and vacuum

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.

Individual and community level factors associated with unintended pregnancy among pregnant women in Ethiopia

Unintended pregnancy is among the major challenges of public health and a major reproductive health issue, due to its implications on the health, economic and social life of a woman and her family mainly in low and middle-income countries, particularly sub-Saharan Africa. The study aimed to assess unintended pregnancy and associated factors among pregnant women in Ethiopia using multilevel analysis from the EDHS 2016. We used the data from the 2016 Ethiopian Demographic and Health Survey, comprised of 1122 pregnant women. The prevalence of unintended pregnancy was determined through descriptive statistics and multilevel logistic regression was performed to identify factors associated with unintended pregnancy. Variables with a p-value < 0.05 in the selected model were considered as significantly associated and an adjusted odds ratio was used to determine the strength and direction of the association. The prevalence of unintended pregnancy was 29.7% (CI 27.0%, 32.4%), of which 20.4% were mistimed and 9.3% unwanted. Being multi-para and fertility preference to have no more child were associated with a higher risk of unintended pregnancy whereas husbands' polygamy relation, having no women autonomy, and living in Afar and Somali regions showed a less likely risk of experiencing an unintended pregnancy. This study showed that the proportion of women who experienced unintended pregnancy is considerably high. Parity, fertility preference, polygamy relation, women autonomy, and region were identified factors associated with unintended pregnancy. Therefore, policymakers at all levels, reproductive health experts, and concerned organizations should emphasize minimizing unintended pregnancy targeting the regional variation at large. Researchers have to explore the regional variations through a qualitative study.

Monogamy and polygamy for generalized W -class states using Rényi- α entropy

We investigate monogamy relations and upper bounds for generalized $W$-class states related to the R\'{e}nyi-$\alpha$ entropy. First, we present an analytical formula on R\'{e}nyi-$\alpha$ entanglement (R$\alpha$E) and R\'{e}nyi-$\alpha$ 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$\alpha$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$\alpha$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$\alpha$E by the analytical expression between R$\alpha$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.

Distribution of the Generalized Correlated Coherence in Tripartite Systems

The generalized correlated coherence is not stored locally, but does exist within the correlations between subsystems. We show that, in tripartite quantum systems, the generalized correlated coherence obeys the polygamy relation when the used coherence measure is strong subadditive. We further provide a sufficient condition, on which the generalized correlated coherence monogamy inequalities hold. These distribution results could just apply to the generalized correlated coherence, but not all quantum coherence.