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Sequential weak measurements of non-commuting observables is not only fundamentally interesting in quantum measurement but also shown potential in various applications. The previous reported methods, however, can only realize limited sequential weak measurements experimentally. In this Letter, we propose the realization of sequential measurements of arbitrary observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables by using genuine single photons. The results presented here will not only improve our understanding of quantum measurement, e.g. testing quantum contextuality, macroscopic realism, and uncertainty relation, but also have many applications such as realizing counterfactual computation, direct process tomography, direct measurement of the density matrix and unbounded randomness certification.
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the
There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG($n, p$), $n$ being odd and $p
The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measur
We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iterativ
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the di