On a Matrix Inequality Related to the Distillability Problem

Abstract

We investigate the distillability problem in quantum information in Cd⊗Cd. One case of the problem has been reduced to proving a matrix inequality when d=4. We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d=4 and for the third family with d≥5. We also present a sufficient condition for the fulfillment of the inequality with d=4.