  Quantum entanglement of pure states is usually quantified via the
entanglement entropy, the von Neumann entropy of the reduced state.
Entanglement entropy is closely related to entanglement distillation, a process
for converting quantum states into singlets, which can then be used for various
quantum technological tasks. The relation between entanglement entropy and
entanglement distillation has been known only for the asymptotic setting, and
the meaning of entanglement entropy in the single-copy regime has so far
remained open. Here we close this gap by considering entanglement catalysis. We
prove that entanglement entropy completely characterizes state transformations
in the presence of entangled catalysts. Our results suggest that catalysis is
useful for a broad range of quantum information protocols, giving asymptotic
results an operational meaning also in the single-copy setup.
