  We show that the maximum fidelity obtained by a p.p.t. distillation protocol
is given by the solution to a certain semidefinite 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 distillable entanglement). In the presence of
symmetry, the semidefinite program simplifies considerably, becoming a linear
program in the case of isotropic and Werner states. Using these techniques, we
determine the p.p.t. distillable entanglement of asymmetric Werner states and
``maximally correlated'' states. We conclude with a discussion of possible
applications of semidefinite programming to quantum codes and 1-local
distillation.
