On the exact variance of Tsallis entropy in a random pure state

Tsallis entropy is a useful one-parameter generalization of the standard von Neumann entropy in information theory. We study the variance of Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proved variance formula of von Neumann entropy based on the derived moment relation to the Tsallis entropy

Symmetry analysis of the hadronic tensor for the semi-inclusive pseudoscalar meson leptoproduction from an unpolarized nucleon target

By examining the symmetry constraints on the semi-inclusive pseudoscalar particle production in unpolarized inelastic lepton-hadron scattering, we present a complete, exact Lorentz decomposition for the corresponding hadronic tensor. As a result, we find that it contains five independent terms, instead of the four as have been suggested before. The newly identified one is odd under the naive time reversal transformation, and the corresponding structure function is directly related to the single spin asymmetry in the semi-inclusive pseudoscalar meson production by a polarized lepton beam off an unpolarized target.Comment: This manuscript is of no use at its present form, so the author withdrew it. Sorry

A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization