Experimental investigation of measurement incompatibility of mutually unbiased bases

Incompatible measurements are of fundamental importance to re-vealing the peculiar features of quantum theory,and are also use-ful resources in various quantum information tasks.In this work,we investigate the quantum incompatibility of mutually unbiased bases(MUBs)within the operational framework of quantum resource the-ory,and report an experimental validation via the task of state dis-crimination.In particular,we construct an experimentally friendly witness to detect incompatible MUBs,based on the probability of cor-rectly discriminating quantum states.Furthermore,we prove that the noise robustness of MUBs can be retrieved from violating the above witness.Finally,we experimentally test the incompatibility of MUBs of dimensionality ranging from 2 to 4,and demonstrate that it is more robust to noise,as either the dimensionality of measurements or the number of MUBs increases.Our results may aid the exploration of the essential roles of incompatible measurements in both theoretical and practical applications in quantum information.