  We analyze approximate transformations of pure entangled quantum states by
local operations and classical communication, finding explicit conversion
strategies which optimize the fidelity of transformation. These results allow
us to determine the most faithful teleportation strategy via an initially
shared partially entangled pure state. They also show that procedures for
entanglement manipulation such as entanglement catalysis [Jonathan and Plenio,
Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states
involved, and motivate the notion of non-local fidelity, which quantifies the
difference in the entangled properties of two quantum states.
