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Local operations on subsystems and classical communication between parties(LOCC) constitute the most general protocols available on spatially separatedquantum systems. Every LOCC protocol implements a separable generalizedmeasurement -- a complete measurement for which every outcome corresponds to atensor product of operators on individual subsystems -- but it is known thatthere exist separable measurements that cannot be implemented by LOCC. Alongstanding problem in quantum information theory is to understand thedifference between LOCC and the full set of separable measurements. In thispaper, we show how to construct an LOCC protocol to implement an arbitraryseparable measurement, except that with those measurements for which no LOCCprotocol exists, the method shows explicitly that this is the case.

When a quantum measurement can be implemented locally ... and when it cannot