Measuring a quantum expectation value of a single qubit without collapse

A well-known feature of quantum mechanics is that measurements on a single quantum state cannot provide full information about its quantum wave function. Determining the expectation value of a quantum observable thus in general requires many copies of the state. This suggests that the wavefunction is given empirical meaning only to an ensemble of identical states. In contrast to this view, Aharonov et al. [1] have proposed a scheme which, under certain conditions, allows one to measure the expectation values of arbitrary observables of a single state without collapsing the wave function. We present the experimental realization of such a protective measurement using a superconducting qubit platform. As an example, our experiment enables full tomographic reconstruction of a single quantum state.



[1] Y. Aharonov, J. Anandan and L. Vaidman, Phys. Rev. A 1993, 47, 4616