Geometry on the set of quantum states and quantum correlations  Dominique Spehner

Author: Dominique Spehner
Institution: Université Joseph Fourier, Grenoble, Institut Fourier, France.
Website: https://wwwfourier.ujfgrenoble.fr/~spehner/
Video: http://www.youtube.com/watch?v=5Nj5afyivI8
Slides: https://drive.google.com/open?id=0B0QKxsVtOaTiR3lWZ1dUSVlhakE
Presentation: https://www.see.asso.fr/node/14277
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
I will show that the set of states of a quantum system with a finitedimensional 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 BogoliubovKuboMori 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.References:
 D. Petz, Monotone Metrics on Matrix Spaces, Lin. Alg. and its Appl. 244, 8196 (1996)
 R. Balian, Y. Alhassid, and H. Reinhardt, Dissipation in manybody systems: a geometric approach based on information theory, Phys. Rep. 131, 1 (1986)
 R. Balian, The entropybased quantum metric, Entropy 2014 16(7), 38783888 (2014)
 A. Uhlmann, The ``transition probability'' in the state space of a *algebra, Rep. Math. Phys. 9, 273279 (1976)
 S.L. Braunstein and C.M. Caves, Statistical Distance and the Geometry of Quantum States, Phys. Rev. Lett. 72, 34393443 (1994)
 D. Spehner, Quantum correlations and Distinguishability of quantum states, J. Math. Phys. 55 (2014), 075211
Bio:
 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, 19951996
 PhD in Theoretical Physics, Université Paul Sabatier, Toulouse, France, 19962000.
 Postdoctoral fellow, Pontificia Universidad Católica, Santiago, Chile, 20002001
 Research Associate, University of DuisburgEssen, Germany, 20012005
 Maître de Conférences, Université Joseph Fourier, Grenoble, France, 2005present
 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