Analysis Seminar

Yiu-Tung Poon, Iowa State University

"(p,q) Matricial Range and Quantum Information Science"

Let M_mn be the set of m x n matrices and write M_n for M_nn. Let V_r={X\in M_nr:X*X=I_r}, where I_r denotes the r x r identity matrix. Suppose   A₁,...,A_m\in M_n and p,q\ge 1.  The (p,q) matricial range of  A₁,...,A_m is given by

$$\Lambda_p,q (A₁,...,A_m)= {(B₁,...,B_m)\in M_q^m: X*A_jX = I_p \otimes B_j with X \in V_pq for j = 1,...,m}.$$

The study of \Lambda_p,q is motivated by problems in quantum error correction. It can also be viewed as extension on some classical subjects, e.g. joint numerical ranges and compression of matrices.  We will discuss some results and problems on \Lambda_p,q.

This is joint work with Pan-Shun Lau,  Chi-Kwong Li, and Nung-Sing Sze.

MC 5417