Rigorous treatment of distillable entanglement

The notion of distillable entanglement is one of the fundamental concepts o f 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 tha t the distillation protocol produce an output of constant dimension. It is therefore conceivable that this unnecessary constraint might have led to un derestimation of the hue distillable entanglement. We give a definition of distillable entanglement which removes this constraint, but could conceivab ly overestimate the true value. Since the definitions turn out to be equiva lent, neither underestimation nor overestimation is possible, and both defi nitions are arguably correct.