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It is well known that when two or more quantum measurements suffer fromimperfections they may lose their incompatibility. For a quantum system offinite dimension d we study the incompatibility of all projective measurementssubjected to white noise and loss. We derive a necessary and sufficientconditions for this set of measurements to becomes compatible in terms of theirvisibility $p$ and efficiency $\eta$.

Compatibility of projective measurements subject to white noise and loss