  We consider the problem of computing the family of operator norms recently
introduced in arXiv:0909.3907. 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 there are
non-positive partial transpose Werner states that are r-undistillable for
arbitrary r. 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.

Quantum Physics