Computing mixed Schatten norm of completely positive maps

09/15/2022

∙

by   Mohammad ShahverdiKondori, et al.

∙

0

∙

share

Computing p → q norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing p → q norm for a matrix with nonnegative entries. Here we define an equivalent iteration method for computing S_p → S_q norm for completely positive maps where S_p is the Schatten p norm. We generalize almost all of the definitions, properties, lemmas, etc. in the matrix setting to completely positive maps and prove an important theorem in this setting.