A FAMILY OF NORMS WITH APPLICATIONS IN QUANTUM INFORMATION THEORY II

作者：Johnston Nathaniel^*; Kribs David W

来源：Quantum Information & Computation, 2011, 11(1-2): 104-123.

• norm
• separability
• Schmidt rank
• bound entanglement

We consider the problem of computing the family of operator norms recently introduced in [1]. We develop a family of semidefinite programs that can be used to exactly compute them in small dimensions and bound them in general. Some theoretical consequences follow from the duality theory of semidefinite programming, including a new constructive proof that for all r there are non-positive partial transpose Werner states that are r-undistillable. Several examples are considered via a MATLAB implementation of the semidefinite program, including the case of Werner states and randomly generated states via the Bures measure, and approximate distributions of the norms are provided. We extend these norms to arbitrary convex mapping cones and explore their implications with positive partial transpose states.

• 出版日期2011-1