10,603 research outputs found
A Maximum Entropy Procedure to Solve Likelihood Equations
In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon\u2019s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth\u2019s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation
Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
A comparison is made of various searching procedures, based upon different
entanglement measures or entanglement indicators, for highly entangled
multi-qubits states. In particular, our present results are compared with those
recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The
statistical distribution of entanglement values for the aforementioned
multi-qubit systems is also explored.Comment: 24 pages, 3 figure
Optimal measurements for nonlocal correlations
A problem in quantum information theory is to find the experimental setup
that maximizes the nonlocality of correlations with respect to some suitable
measure such as the violation of Bell inequalities. The latter has however some
drawbacks. First and foremost it is unfeasible to determine the whole set of
Bell inequalities already for a few measurements and thus unfeasible to find
the experimental setup maximizing their violation. Second, the Bell violation
suffers from an ambiguity stemming from the choice of the normalization of the
Bell coefficients. An alternative measure of nonlocality with a direct
information-theoretic interpretation is the minimal amount of classical
communication required for simulating nonlocal correlations. In the case of
many instances simulated in parallel, the minimal communication cost per
instance is called nonlocal capacity, and its computation can be reduced to a
convex-optimization problem. This quantity can be computed for a higher number
of measurements and turns out to be useful for finding the optimal experimental
setup. Focusing on the bipartite case, in this paper, we present a simple
method for maximizing the nonlocal capacity over a given configuration space
and, in particular, over a set of possible measurements, yielding the
corresponding optimal setup. Furthermore, we show that there is a functional
relationship between Bell violation and nonlocal capacity. The method is
illustrated with numerical tests and compared with the maximization of the
violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit
as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed
by qutrits turns out to be even stronger if the nonlocal capacity is employed
as a measure of nonlocality.Comment: Some typos and errors have been corrected, especially in the section
concerning the relation between Bell violation and communication complexit
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