  We investigate quantum phase transitions and quantum coherence in infinite
biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All
considered coherence measures such as the $l_1$ norm of coherence, the relative
entropy of coherence, and the quantum Jensen-Shannon divergence, and the
quantum mutual information show consistently that singular behaviors occur for
the spin-1 system, which enables to identity quantum phase transitions. For the
spin-2 system, the relative entropy of coherence and the quantum mutual
information properly detect no singular behavior in the whole system parameter
range, while the $l_1$ norm of coherence and the quantum Jensen-Shannon
divergence show a conflicting singular behavior of their first-order
derivatives. Examining local magnetic moments and spin quadrupole moments lead
to the explicit identification of novel orderings of spin quadrupole moments
with zero magnetic moments in the whole parameter space. We find the three
uniaxial spin nematic quadrupole phases for the spin-1 system and the two
biaxial spin nematic phases for the spin-2 system. For the spin-2 system, the
two orthogonal biaxial spin nematic states are connected adiabatically without
an explicit phase transition, which can be called quantum crossover. The
quantum crossover region is estimated by using the quantum fidelity. Whereas
for the spin-1 system, the two discontinuous quantum phase transitions occur
between three distinct uniaxial spin nematic phases. We discuss the quantum
coherence measures and the quantum mutual information in connection with the
quantum phase transitions including the quantum crossover.
