On a matrix inequality related to the distillability problem

Abstract

We investigate the distillability problem in quantum information in $\bbC^d\ox\bbC^d$. A special case of the problem has been reduced to proving a matrix inequality when $d=4$. We investigate the inequality for two families of non-normal matrices. We prove the inequality for the first family with $d=4$ and two special cases of the second family with $d\ge 4$. We also prove the inequality for all normal matrices with $d>4$.

19 pages, comments are welcome

References in corpus (4)

• Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs
• Rank three bipartite entangled states are distillable
• Non-positive-partial-transpose quantum states of rank four are distillable
• A gap for PPT entanglement

Cited by in corpus (1)

• A matrix inequality related to the entanglement distillation problem