  A general law is presented for (composite) quantum systems which directly
describes the time evolution of quantum states (with one or both components)
through an arbitrary noisy quantum channel. It is shown that the time evolution
of all quantum states through a quantum channel can be completely captured by
the evolution of a single 'probe state'. Thus in order to grasp the information
of the final output states subject to a quantum channel, especially an unknown
one, it only requires quantum state tomography of a single probe state, which
dramatically simplifies the practical operations in experiment.
