  Measuring a quantum system can randomly perturb its state. The strength and
nature of this back-action depends on the quantity which is measured. In a
partial measurement performed by an ideal apparatus, quantum physics predicts
that the system remains in a pure state whose evolution can be tracked
perfectly from the measurement record. We demonstrate this property using a
superconducting qubit dispersively coupled to a cavity traversed by a microwave
signal. The back-action on the qubit state of a single measurement of both
signal quadratures is observed and shown to produce a stochastic operation
whose action is determined by the measurement result. This accurate monitoring
of a qubit state is an essential prerequisite for measurement-based feedback
control of quantum systems.
