Rigorous treatment of distillable entanglement

The notion of distillable entanglement is one of the fundamental concepts of quantum information theory. Unfortunately, there is an apparent mismatch between the intuitive and rigorous definitions of distillable entanglement. To be precise, the existing rigorous definitions impose the constraint that the distillation protocol produce an output of constant dimension. It is therefore conceivable that this unnecessary constraint might have led to underestimation of the true distillable entanglement. We give a definition of distillable entanglement which removes this constraint, but could conceivably overestimate the true value. Since the definitions turn out to be equivalent, neither underestimation nor overestimation is possible, and both definitions are arguably correct.