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We prove a necessary condition that a quantum channel on a multipartitesystem may be approximated arbitrarily closely using local operations andclassical communication (LOCC). We then extend those arguments to obtain acondition that applies to all quantum instruments, which range from the mostrefined case, a generalized measurement, to the most coarse-grained, which is aquantum channel. We illustrate these results by a detailed analysis of aquantum instrument that is known not to be implementable by LOCC, but which canbe arbitrarily closely approximated within that framework. As one outgrowth ofthis analysis, we find a quantum measurement that falls into the same category:it cannot be implemented exactly by LOCC, but can be approximated by LOCCarbitrarily closely. This measurement has an infinite number of outcomes,leaving open the question as to whether or not there exists a measurementwithin this same category but having only a finite number of outcomes.

Asymptotic implementation of multipartite quantum channels and other quantum instruments using local operations and classical communication