  The cores of neutron stars (NSs) near the maximum mass realize the most
highly compressed matter in the universe where quark degrees of freedom may be
liberated. Such a state of dense matter is hypothesized as quark matter (QM)
and its presence has awaited to be confirmed for decades in nuclear physics.
Gravitational waves from binary NS mergers are expected to convey useful
information called the equation of state (EOS). However, the signature for QM
with realistic EOS is not yet established. Here, we show that the gravitational
wave in the post-merger stage can distinguish the theory scenarios with and
without a transition to QM. Instead of adopting specific EOSs as studied
previously, we compile reliable EOS constraints from the ab initio approaches.
We demonstrate that early collapse to a black hole after NS merger signifies
softening of the EOS associated with the onset of QM in accord with ab initio
constraints. Nature of hadron-quark phase transition can be further constrained
by the condition that electromagnetic counterparts need to be energized by the
material left outside the remnant black hole.
