Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

The Parallel Image Processing System PIPS - An open, scalable Image Processing Library for massively parallel systems

PIPS is a parallel image processing system developed at the TU Hamburg-Harburg 1 . The structure of PIPS is highly modular and hierarchical. The scope of the PIPS functionality reaches from basic low level services up to high end user interfaces. PIPS is based on the message passing principle and is therefore portable to most distributed memory architectures. A wide range of library functions, along with implementations of many typical image processing algorithms, make it easy to integrate new parallel algorithms into PIPS. Using the high end interfaces the user views the parallel system as a powerful coprocessor attached to the host machine. The parallel image processing system PIPS has been developed 1 as a platform for research in the field of image processing and parallel computing [4, 2, 5]. Image processing algorithms are well suited for parallel systems due to the large amount of data and the possibility to distribute the calculations on many processors in a natural way. A..