  Quantum state tomography is an important tool for quantum communication,
computation, metrology, and simulation. Efficient quantum state tomography on a
high dimensional quantum system is still a challenging problem. Here, we
propose a novel quantum state tomography method, auxiliary Hilbert space
tomography, to avoid pre-rotations before measurement in a quantum state
tomography experiment. Our method requires projective measurements in a higher
dimensional space that contains the subspace that includes the prepared states.
We experimentally demonstrate this method with orbital angular momentum states
of photons. In our experiment, the quantum state tomography measurements are as
simple as taking a photograph with a camera. We experimentally verify our
method with near-pure- and mixed-states of orbital angular momentum with
dimension up to $d=13$, and achieve greater than 95 % state fidelities for all
states tested. This method dramatically reduces the complexity of measurements
for full quantum state tomography, and shows potential application in various
high dimensional quantum information tasks.
