  Many quantum information protocols rely on optical interference to compare
datasets with efficiency or security unattainable by classical means. Standard
implementations exploit first-order coherence between signals whose preparation
requires a shared phase reference. Here, we analyze and experimentally
demonstrate binary discrimination of visibility hypotheses based on
higher-order interference for optical signals with a random relative phase.
This provides a robust protocol implementation primitive when a phase lock is
unavailable or impractical. With the primitive cost quantified by the total
detected optical energy, optimal operation is typically reached in the
few-photon regime.
