We study a general teleportation scheme with an arbitrary state of the pair of particles $(2$ and $3)$ shared by Alice and Bob, and arbitrary measurements on the input particle 1 and one of the members (2) of the pair on Alice's side. We find an efficient iterative algorithm for identifying optimum operations on Bob's side. In particular, we find that simple unitary transformations on his side are not always optimal even if particles 2 and 3 are perfectly entangled. We describe the most interesting protocols in the language of extremal completely positive maps.
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Řeháček et al. (2001) studied this question.
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