How to exploit local information when distilling entanglement

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.