Two important classes of manifolds of quantum states, the locally quasi-classical manifold and the quasi-classical manifold, are introduced from the estimation theoretical viewpoint, and they are characterized geometrically by the vanishing conditions of the relative phase factor (RPF), implying the close tie between Uhlmann parallel transport and the quantum estimation theory.

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these converge superlinearly, corresponding rates still remain unknown. In this paper, we address problem. obtain first explicit non-asymptotic superlinear standard methods, which are based on updating formulas from convex Broyden clas...

A frequently encountered source of systematic error in quantum computations is imperfections the control pulses which are classical fields that qubit gate operations. From an analysis mechanical time-evolution operator spin wavefunction, it has been demonstrated composite can mitigate certain errors and appealing geometric interpretation was developed for design error-suppressing pulses. Here w...

We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action – the critical value of the Liouville action functional, considered as a function on the quasiFuchsian deformation space, is an antiderivative of a 1-form ...