  The use of ancillary quantum systems known as catalysts is known to be able
to enhance the capabilities of entanglement transformations under local
operations and classical communication. However, the limits of these advantages
have not been determined, and in particular it is not known if such assistance
can overcome the known restrictions on asymptotic transformation rates --
notably the existence of bound entangled (undistillable) states. Here we
establish a general limitation of entanglement catalysis: we show that
catalytic transformations can never allow for the distillation of entanglement
from a bound entangled state with positive partial transpose, even if the
catalyst may become correlated with the system of interest, and even under
permissive choices of free operations. This precludes the possibility that
catalysis can make entanglement theory asymptotically reversible. Our methods
are based on new asymptotic bounds for the distillable entanglement and
entanglement cost assisted by correlated catalysts.
