  We present a systematic and complementary study of quantum correlations near
a black hole by considering the measurement-induced nonlocality (MIN). The
quantum measure of interest is discussed on the same footing for the fermionic,
bosonic and mixed fermion-boson modes in relation to the Hawking radiation. The
obtained results show that in the infinite Hawking temperature limit, the
physically accessible correlations does not vanish only in the fermionic case.
However, the higher frequency modes can sustain correlations for the finite
Hawking temperature, with mixed system being more sensitive towards increase of
the fermionic frequencies than the bosonic ones. Since the MIN for the latter
modes quickly diminishes, the increased frequency may be a way to maintain
nonlocal correlations for the scenarios at the finite Hawking temperature.
