40,893 research outputs found
A comparison of computational methods and algorithms for the complex gamma function
A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries
Symbolic integration of a class of algebraic functions
An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions
A numerical table of Lommel functions with two imaginary arguments
Numerical table of Lommel functions with two imaginary argument
Critique of proposed limit to space--time measurement, based on Wigner's clocks and mirrors
Based on a relation between inertial time intervals and the Riemannian
curvature, we show that space--time uncertainty derived by Ng and van Dam
implies absurd uncertainties of the Riemannian curvature.Comment: 5 pages, LaTex, field "Author:" correcte
A simple minimax estimator for quantum states
Quantum tomography requires repeated measurements of many copies of the
physical system, all prepared by a source in the unknown state. In the limit of
very many copies measured, the often-used maximum-likelihood (ML) method for
converting the gathered data into an estimate of the state works very well. For
smaller data sets, however, it often suffers from problems of rank deficiency
in the estimated state. For many systems of relevance for quantum information
processing, the preparation of a very large number of copies of the same
quantum state is still a technological challenge, which motivates us to look
for estimation strategies that perform well even when there is not much data.
In this article, we review the concept of minimax state estimation, and use
minimax ideas to construct a simple estimator for quantum states. We
demonstrate that, for the case of tomography of a single qubit, our estimator
significantly outperforms the ML estimator for small number of copies of the
state measured. Our estimator is always full-rank, and furthermore, has a
natural dependence on the number of copies measured, which is missing in the ML
estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and
an additional appendix on symmetric measurement
- …