Experimental investigation of maximum-confidence measurements and their contextual advantages

Nonorthogonal quantum states cannot be perfectly distinguished; seeking the optimal discrimination strategy is a critical task in quantum information processing. Maximum-confidence measurements provide the highest confidence that represents the conditional probability of the prepared state being correct given an observed outcome. In this work, we experimentally investigate maximum-confidence measurements by discrete-time quantum walks for geometrically uniform states and tetrahedron states, and our experimental results clearly show that the maximum-confidence measurements coincide with minimum-error discrimination in these cases. Meanwhile, we also provide experimental evidence for the contextual advantage of maximum-confidence measurements in quantum theory over classical theory, using two quantum pure states as an example. Our work provides a unified experimental approach to quantum state discrimination that highlights the practical value of maximum-confidence measurements in quantum information processing.