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Sequential weak measurements of non-commuting observables is not onlyfundamentally interesting in quantum measurement but also shown potential invarious applications. The previous reported methods, however, can only realizelimited sequential weak measurements experimentally. In this Letter, we proposethe realization of sequential measurements of arbitrary observables andexperimentally demonstrate for the first time the measurement of sequentialweak values of three non-commuting Pauli observables by using genuine singlephotons. The results presented here will not only improve our understanding ofquantum measurement, e.g. testing quantum contextuality, macroscopic realism,and uncertainty relation, but also have many applications such as realizingcounterfactual computation, direct process tomography, direct measurement ofthe density matrix and unbounded randomness certification.

Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables