[QIP-Sem] QIP Seminar at Northeastern University

[Timothy F. Havel]

The following QIP seminar, which will take place on Tuesday September 
20 at 14:00 hours in 509 Lake Hall (Northeastern University), may be 
of interest to the readers of this list.


Norm Compression Inequalities for Block Matrices
(Northeastern University's Probability, Statistics and Applications Seminar)

by Koenraad Audenaert (Imperial College London)

ABSTRACT

I consider inequalities for the Schatten q-norms, which are 
non-commutative generalistions of the l_q norms. Given a block 
partitioned matrix, one can try and bound the q-norm of the matrix 
itself in terms of the q-norms of the blocks. The inequalities that 
arise can be called norm compression inequalities, because the bound 
is stated in terms of the elements of the norm compression of the 
matrix, which is what you get when replacing every block of the 
matrix by its norm. In this talk I give an overview of previously 
known bounds of this kind. I then present some norm compression 
bounds for positive semidefinite 2X2 block matrices, complementing 
earlier work by Chris King. Finally, I give an overview of various 
conjectured norm compression inequalities, and discuss some of the 
implications their validity would have in quantum information theory.

See also math.FA/0505680
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