Geometry on the set of quantum states and quantum correlations - Dominique Spehner
Author: Dominique Spehner
Institution: Université Joseph Fourier, Grenoble, Institut Fourier, France.
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I will show that the set of states of a quantum system with a finite-dimensional Hilbert space can be equipped with various Riemannian distances having nice properties from a quantum information viewpoint, namely they are contractive under all physically allowed operations on the system. The corresponding metrics are quantum analogs of the Fisher metric and have been classified by D. Petz. Two distances are particularly relevant physically: the Bogoliubov-Kubo-Mori distance studied by R. Balian, Y. Alhassid and H. Reinhardt, and the Bures distance studied by A. Uhlmann and by S.L. Braunstein and C.M. Caves. The latter gives the quantum Fisher information playing an important role in quantum metrology. A way to measure the amount of quantum correlations (entanglement or quantum discord) in bipartite systems (that is, systems composed of two parties) with the help of these distances will be also discussed.
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- Diplôme d'Études Approfondies (DEA) in Theoretical Physics at the École Normale Supérieure de Lyon, 1994
- Civil Service (Service National de la Coopération), Technion Institute of Technology, Haifa, Israel, 1995-1996
- PhD in Theoretical Physics, Université Paul Sabatier, Toulouse, France, 1996-2000.
- Postdoctoral fellow, Pontificia Universidad Católica, Santiago, Chile, 2000-2001
- Research Associate, University of Duisburg-Essen, Germany, 2001-2005
- Maître de Conférences, Université Joseph Fourier, Grenoble, France, 2005-present
- Habilitation à diriger des Recherches (HDR), Université Grenoble Alpes, 2015
- Member of the Institut Fourier (since 2005) and the Laboratoire de Physique et Modélisation des Milieux Condensés (since 2013) of the university Grenoble Alpes, France