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We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. quant-ph/0102043 states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.
Eggeling et al. (Fri,) studied this question.