Belt distance between facets of space-filling zonotopes

For every d-dimensional polytope P with centrally symmetric facets we can associate a "subway map" such that every line of this "subway" corresponds to set of facets parallel to one of ridges P. The belt diameter of P is the maximal number of line changes that you need to do in order to get from one station to another. In this paper we prove that belt diameter of d-dimensional space-filling zonotope is not greater than $\lceil \log_2\frac45d\rceil$. Moreover we show that this bound can not be improved in dimensions d at most 6.Comment: 17 pages, 5 figure

Entanglement Swapping: Entangling Atoms That Never Interacted

In this paper we discuss four different proposals of entangling atomic states of particles which have never interacted. The experimental realization proposed makes use of the interaction of Rydberg atoms with a micromaser cavity prepared in either a coherent state or in a superposition of the zero and one field Fock states. We consider atoms in either a three-level cascade or lambda configurationComment: 17 pages and 2 figure