  Quantum coherence is a fundamental feature of quantum physics and plays a
significant role in quantum information processing. By generalizing the
resource theory of coherence from von Neumann measurements to positive
operator-valued measures (POVMs), POVM-based coherence measures have been
proposed with respect to the relative entropy of coherence, the $l_1$ norm of
coherence, the robustness of coherence and the Tsallis relative entropy of
coherence. We derive analytically the lower and upper bounds on these
POVM-based coherence of an arbitrary given superposed pure state in terms of
the POVM-based coherence of the states in superposition. Our results can be
used to estimate range of quantum coherence of superposed states. Detailed
examples are presented to verify our analytical bounds.
