On thurston's core entropy algorithm dedicated to the memory of tan lei

The core entropy of polynomials, recently introduced by W. Thurston, is a dy-namical invariant extending topological entropy for real maps to complex polynomials, whence providing a new tool to study the parameter space of polynomials. The base is a combinatorial algorithm allowing for the computation of the core entropy given by Thurston, but without supplying a proof. In this paper, we will describe his algorithm and prove its validity

Wandering continua for rational maps

We prove that a Latt' es map admits an eventually simply-connected wandering continuum precisely when it is flexible. The simply-connected wandering continuum is a line segment in a bi-infinite geodesic under the flat metric

Teleporting a quantum state in a subset of the whole Hilbert space

We investigate the lower bound of the amount of entanglement for faithfully teleporting a quantum state belonging to a subset of the whole Hilbert space. Moreover, when the quantum state belongs to a set composed of two states, a probabilistic teleportation scheme is presented using a non-maximally entangled state as the quantum channel. We also calculate the average transmission efficiency of this scheme.Comment: 4 pages, no figur