  The quantum component in uncertainty relation can be naturally characterized
by the quantum coherence of a quantum state, which is of paramount importance
in quantum information science. Here, we experimentally investigate quantum
uncertainty relations construed with relative entropy of coherence, $l_1$ norm
of coherence and coherence of formation. In stead of quantum state tomographic
technology, we employ the classical shadow algorithm for the detection of lower
bounds in quantum uncertainty relations. With an all optical setup, we prepare
a family of quantum states whose purity can be fully controlled. We
experimentally explore the tightness of various lower bounds in different
reference bases on the prepared states. Our results indicate the tightness of
quantum coherence lower bounds dependents on the reference bases as well as the
purity of quantum state.

Quantum Physics