  It is known that general convertibility of bipartite entangled states is not
possible to arbitrary error without some classical communication. While some
trade-offs between communication cost and conversion error have been proven,
these bounds can be very loose. In particular, there are many cases in which
tolerable error might be achievable using zero-communication protocols. In this
work we address these cases by deriving the optimal fidelity of pure state
conversions under local unitaries as well as local operations and shared
randomness (LOSR). We also uses these results to explore catalytic conversions
between pure states using zero communication.
