Reading List: It is suggested that all participants do some preliminary reading before coming to the workshop. The following sources will be helpful: 1. R. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Chapters 1,2,3, Chapter 4 Sections 4-6, Chapter 7. 2. R. Horn and C. R. Johnson, Topics in Matrix Analysis Chapter 3, Sections 0-1. 3. R. Bhatia, Positive Definite Matrices, Princeton University Press. (Familiarity with topics covered here will be useful for the Matrix Analysis, and Quantum Information Theory lectures). 4. R Bhatia, Pinching,trimming,truncating and averaging of matrices, paper available on the course website. ------------------------------------------------------------ Useful preparation for the course "Numerical ranges (classical and higher-rank) with applications to quantum information theory" , to be given by John Holbrook during the second week, might include some familiarity with: 1. Gustafson and Rao, "Numerical Range", Springer 1997 2. David W. Kribs, "A quantum computing primer for operator theorists" (may be downloaded from Kribs' publications website) 3. The recent book by Denes Petz, "Quantum Information Theory and Quantum Statistics" (published by Springer) 4. Chi-Kwong Li and Nung-Sing Sze, "Canonical forms, higher rank numerical range, convexity, totally isometric subspace, matrix equations" 2007 (may be downloaded from Li's publication website) ------------------------------------------------------------ References in connection with the lectures by Mary Beth Ruskai on: "Properties of quantum entropy and related concave trace functions" include: "Inequalities for Quantum Entropy: A Review with Conditions for Equality" J. Math. Phys. 43, 4358-4375 (2002); erratum 46, 019901 (2005). (quant-ph/0205064) "Lieb's simple proof of concavity of Tr Ap K† B(1-p) K and remarks on related inequalities" Internat. Jour. Quant. Info 3, 570--590 (2005); erratum 4, 747-748 (2006) quant-ph/0404126 "Another short and elementary proof of strong subadditivity of quantum entropy" Reports on Mathematical Physics 60, 1-12 (2007). quant-ph/0604206 "Unified Treatment of Convexity of Relative Entropy and Related Trace Functions, with Conditions for Equality" submitted for publication [with A. Jencova].arXiv:0903.2895

Organizers

Directors: R. Bhatia, J. Holbrook, S. Serra Capizzano. Local Organizer: R.T. Ramakrishnan