Optimal measurements to access classical correlations of two-qubit states

We analyze the optimal measurements accessing classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the probability distribution of the optimal measurements. The probability distribution of the optimal measurement is found to be centralized in the vicinity of a specific von Neumann measurement, which we call the maximal-correlation-direction measurement (MCDM). We prove that for the states with zero-discord and maximally mixed marginals, the MCDM is the very optimal measurement. Furthermore, we give an upper bound of quantum discord based on the MCDM, and investigate its performance for approximating the quantum discord.Comment: 8 pages, 3 figures, version accepted by Phys. Rev.

Dynamics of multipartite quantum correlations under decoherence

Quantum discord is an optimal resource for the quantification of classical and non-classical correlations as compared to other related measures. Geometric measure of quantum discord is another measure of quantum correlations. Recently, the geometric quantum discord for multipartite states has been introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have investigated global quantum discord (QD) and geometric quantum discord (GQD) under the influence of external environments for different multipartite states. Werner-GHZ type three-qubit and six-qubit states are considered in inertial and non-inertial settings. The dynamics of QD and GQD is investigated under amplitude damping, phase damping, depolarizing and flipping channels. It is seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ states and for p>0.5 for six qubit GHZ states. This implies that multipartite states are more fragile to decoherence for higher values of N. Surprisingly, a rapid sudden death of discord occurs in case of phase flip channel. However, for bit flip channel, no sudden death happens for the six-qubit states. On the other hand, depolarizing channel heavily influences the QD and GQD as compared to the amplitude damping channel. It means that the depolarizing channel has the most destructive influence on the discords for multipartite states. From the perspective of accelerated observers, it is seen that effect of environment on QD and GQD is much stronger than that of the acceleration of non-inertial frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore, QD exhibits more robustness than GQD when the multipartite systems are exposed to environment.Comment: 15 pages, 4 figures, 4 table

Nonparametric Estimation of Copula Regression Models With Discrete Outcomes

Multivariate discrete outcomes are common in a wide range of areas including insurance, finance, and biology. When the interplay between outcomes is significant, quantifying dependencies among interrelated variables is of great importance. Due to their ability to accommodate dependence flexibly, copulas are being applied increasingly. Yet, the application of copulas on discrete data is still in its infancy; one of the biggest barriers is the nonuniqueness of copulas, calling into question model interpretations and predictions. In this article, we study copula estimation with discrete outcomes in a regression context. As the marginal distributions vary with covariates, inclusion of continuous regressors expands the region of support for consistent estimation of copulas. Because some properties of continuous outcomes do not carry over to discrete outcomes, specification of a copula model has been a problem. We propose a nonparametric estimator of copulas to identify the “hidden” dependence structure for discrete outcomes and develop its asymptotic properties. The proposed nonparametric estimator can also serve as a diagnostic tool for selecting a parametric form for copulas. In the simulation study, we explore the performance of the proposed estimator under different scenarios and provide guidance on when the choice of copulas is important. The performance of the estimator improves as discreteness diminishes. A practical bandwidth selector is also proposed. An empirical analysis examines a dataset from the Local Government Property Insurance Fund (LGPIF) in the state of Wisconsin. We apply the nonparametric estimator to model the dependence among claim frequencies from different types of insurance coverage