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The physical nature of any quantum source guarantees the existence of aneffective Hilbert space of finite dimension, the physical sector, in which itsstate is completely characterized with arbitrarily high accuracy. Theextraction of this sector is essential for state tomography. We show that thephysical sector of a state, defined in some pre-chosen basis, can besystematically retrieved with a procedure using only data collected from a setof commuting quantum measurement outcomes, with no other assumptions about thesource. We demonstrate the versatility and efficiency of the physical-sectorextraction by applying it to simulated and experimental data for quantum lightsources, as well as quantum systems of finite dimensions.

Extracting the physical sector of quantum states