On a Matrix Inequality Related to the Distillability Problem

Abstract

We investigate the distillability problem in quantum information in ℂ d ⊗ ℂ d . 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 .

Keywords

• matrix inequality
• singular value
• eigenvalue
• Kronecker product
• quantum information
• distillability problem