  The physical nature of any quantum source guarantees the existence of an
effective Hilbert space of finite dimension, the physical sector, in which its
state is completely characterized with arbitrarily high accuracy. The
extraction of this sector is essential for state tomography. We show that the
physical sector of a state, defined in some pre-chosen basis, can be
systematically retrieved with a procedure using only data collected from a set
of commuting quantum measurement outcomes, with no other assumptions about the
source. We demonstrate the versatility and efficiency of the physical-sector
extraction by applying it to simulated and experimental data for quantum light
sources, as well as quantum systems of finite dimensions.
