  The goal of entanglement distillation is to turn a large number of weakly
entangled states into a smaller number of highly entangled ones. Practical
entanglement distillation schemes offer a tradeoff between the fidelity to the
target state, and the probability of successful distillation. Exploiting such
tradeoffs is of interest in the design of quantum repeater protocols. Here, we
present a number of methods to assess and optimize entanglement distillation
schemes. We start by giving a numerical method to compute upper bounds on the
maximum achievable fidelity for a desired probability of success. We show that
this method performs well for many known examples by comparing it to well-known
distillation protocols. This allows us to show optimality for many well-known
distillation protocols for specific states of interest. As an example, we
analytically prove optimality of the distillation protocol utilized within the
Extreme Photon Loss (EPL) entanglement generation scheme, even in the
asymptotic limit. We proceed to present a numerical method that can improve an
existing distillation scheme for a given input state, and we present an example
for which this method finds an optimal distillation protocol. An implementation
of our numerical methods is available as a Julia package.
