  Quantum state tomography is the experimental procedure of determining an
unknown state. It is not only essential for the verification of resources and
processors of quantum information but is also important in its own right with
regard to the foundation of quantum mechanics. Standard methods have been
elusive for large systems because of the enormous number of observables to be
measured and the exponential complexity of data post-processing. Here, we
propose a new scheme of quantum state tomography that requires the measurement
of only three observables (acting jointly on the system and pointer) regardless
of the size of the system. The system is coupled to a "pointer" of single
qubit, and the wavefunction of the system is "reaped" onto the pointer upon the
measurement of the system. Subsequently, standard two-state tomography on the
pointer and classical post-processing are used to reconstruct the quantum state
of the system. We also developed an efficient and scalable iterative maximum
likelihood algorithm to estimate states from statistically incomplete data.
