


Start Time:
22 June 2009 at 08:30
Ends On:
10 July 2009
Location:
Trieste  Italy
Venue:
AGH (Kastler Lecture Hall)
Organizer(s):
Directors: R. Bhatia, J. Holbrook, S. Serra Capizzano. Local Organizer: R.T. Ramakrishnan
Description:
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 46, Chapter 7.
2. R. Horn and C. R. Johnson, Topics in Matrix Analysis Chapter 3, Sections 01.
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 higherrank) 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. ChiKwong Li and NungSing 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, 43584375 (2002); erratum 46, 019901 (2005). (quantph/0205064)
"Lieb's simple proof of concavity of Tr Ap K† B(1p) K and remarks on related inequalities" Internat. Jour. Quant. Info 3, 570590 (2005); erratum 4, 747748 (2006) quantph/0404126
"Another short and elementary proof of strong subadditivity of quantum entropy" Reports on Mathematical Physics 60, 112 (2007). quantph/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
Material:
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