  Quantum state tomography is the conventional method used to characterize
density matrices for general quantum states. However, the data acquisition time
generally scales linearly with the dimension of the Hilbert space, hindering
the possibility of dynamic monitoring of a high-dimensional quantum system.
Here, we demonstrate a direct tomography protocol to measure density matrices
in the spatial domain through the use of a polarization-resolving camera, where
the dimension of density matrices can be as large as 580$\times$580 in our
experiment. The use of the polarization-resolving camera enables parallel
measurements in the position and polarization basis and as a result, the data
acquisition time of our protocol does not increase with the dimension of the
Hilbert space and is solely determined by the camera exposure time (on the
order of 10 milliseconds). Our method is potentially useful for the real-time
monitoring of the dynamics of quantum states and paves the way for the
development of high-dimensional, time-efficient quantum metrology techniques.
