Experimental Investigation of Quantum Uncertainty Relations With Classical Shadows

Abstract

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, (Formula presented.) norm of coherence, and coherence of formation. Instead 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 that the tightness of quantum coherence lower bounds depends on the reference bases and the purity of the quantum state.