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Two quantum systems are identically prepared in different locations. An observer's task is to determine their state. A simple example shows that a pair of measurements of the von Neumann type is less effective than a sequence of nonorthogonal probability-operator measures, alternating between the two quantum systems. However, the most efficient set of operations of that type that we were able to design falls short of a single combined measurement, performed on both system together.
Peres et al. (Mon,) studied this question.
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