Reexamination of quantum state transformations with zero communication

It is known that general convertibility of bipartite entangled states is not possible to arbitrary error without some classical communication. While some tradeoffs 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 quantum state conversions under local unitaries as well as local operations and shared randomness. We also use these results to explore catalytic conversions between pure states using zero communication.