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

[cschreiner]

Author: Dominique Spehner
Institution: Université Joseph Fourier, Grenoble, Institut Fourier, France.
Website: https://www-fourier.ujf-grenoble.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 Attribution-ShareAlike 4.0 International

Abstract:
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.

References:

• D. Petz, Monotone Metrics on Matrix Spaces, Lin. Alg. and its Appl. 244, 81-96 (1996)
• R. Balian, Y. Alhassid, and H. Reinhardt, Dissipation in many-body systems: a geometric approach based on information theory, Phys. Rep. 131, 1 (1986)
• R. Balian, The entropy-based quantum metric, Entropy 2014 16(7), 3878-3888 (2014)
• A. Uhlmann, The ``transition probability'' in the state space of a *-algebra, Rep. Math. Phys. 9, 273-279 (1976)
• S.L. Braunstein and C.M. Caves, Statistical Distance and the Geometry of Quantum States, Phys. Rev. Lett. 72, 3439-3443 (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, 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