Experimental quantification of quantum coherence for a set of quantum states

We present direct experimental verification of quantum coherence for a set of quantum states in a basis-independent manner. We find that the theory of quantum coherence for a set of quantum states matches our experimental results perfectly and can be applied to protocols such as the 1984 protocol of Bennett and Brassard (BB84) and quantum secure direct communication. Using a Sagnac interferometer, we experimentally quantify the quantum coherence for two sets of experimental states. Moreover, we introduce an application of set coherence, illustrating that the states employed in the BB84 protocol exhibit maximal set coherence. Our results pave the way for wider applications of quantum coherence for a set of quantum states, including quantum key distribution protocols and probabilistic quantum cloning.