  Quantum measurements are described as instantaneous projections in textbooks.
They can be stretched out in time using weak measurements, whereby one can
observe the evolution of a quantum state as it heads towards one of the
eigenstates of the measured operator. This evolution can be understood as a
continuous nonlinear stochastic process, generating an ensemble of quantum
trajectories, consisting of noisy fluctuations on top of geodesics that attract
the quantum state towards the measured operator eigenstates. The rate of
evolution is specific to each system-apparatus pair, and the Born rule
constraint requires the magnitudes of the noise and the attraction to be
precisely related. We experimentally observe the entire quantum trajectory
distribution for weak measurements of a superconducting qubit in circuit QED
architecture, quantify it, and demonstrate that it agrees very well with the
predictions of a single-parameter white-noise stochastic process. This
characterisation of quantum trajectories is a powerful clue to unraveling the
dynamics of quantum measurement, beyond the conventional axiomatic quantum
theory.
