  Distillation protocols enable generation of high quality entanglement even in
the presence of noise. Existing protocols ignore the presence of local
information in mixed states produced from some noise sources such as photon
loss, amplitude damping or thermalization. We propose new protocols that
exploit local information in mixed states. Our protocols converge to higher
fidelities in fewer rounds, and when local information is significant one of
our protocols consistently improves yields by 10 fold or more. We demonstrate
that our protocols can be compacted into an entanglement-pumping scheme,
allowing quantum computation in distributed systems with a few qubits per
location.
