Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Attempts to extend Shannon's noisy coding theorem to a quantum setting have led to interesting mathematical questions concerning products of completely positive maps on matrix algebras. Specifically for trace-preserving maps it is conjectured that the output state with minimal entropy is always a product state -- this is equivalent to the statement that minimal output entropy is additive for such maps. I will review the background to this problem, and describe its relation to some inequalities that arose in different contexts, including strong subadditivity and Hanner's inequality. I will then show how some new matrix inequalities can be used to prove special cases of this result.