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Erschienen in:
01.07.2015
Perfect discrimination of projective measurements with the rank of all projectors being one
Erschienen in: Quantum Information Processing | Ausgabe 7/2015
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Abstract
In this paper, we focus on the global discrimination of projective measurements in which the rank of all projectors is one. Firstly, the relation between single-qubit observables and measurement–unitary operation–measurement scheme (M–U–M scheme) is studied. We show that single-qubit observables can generally not be perfectly discriminated by the M–U–M scheme, and the dimension is the most essential reason. Moreover, when we only consider that projective measurements on \(m\)-dimensional space with \(m\ge 3\) are perfectly discriminated by the M–U–M scheme, the concrete form of the general unitary matrix is presented, which improves the previous results. Lastly, these results are applied to perfectly distinguish projective measurements with the rank of all projectors being one.