A semidefinite program for distillable entanglement

We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semide finite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillab le entanglement). In the presence of symmetry, the semidefinite program sim plifies considerably, becoming a linear program in the case of isotropic an d Werner states. Using these techniques, we determine the p.p.t. distillabl e entanglement of asymmetric Werner states and "maximally correlated" state s. We conclude with a discussion of possible applications of semidefinite p rogramming to quantum codes and 1-local distillation.