Characterization-free classification and identification of the environment between two quantum players

Classifying the causal structure of quantum channels is essential for verifying quantum networks and certifying quantum resources. We introduce a characterization-free protocol enabling two isolated players, Alice and Bob, to classify and identify the definite-order strategy adopted by an unknown environment mediating their channels. Without assuming knowledge of their devices or the environment, the players infer the causal order solely from input-output statistics by testing Markovian conditions that we prove are necessary and sufficient for each strategy class. Remarkably, we prove that even with a minimal random channel consisting of two-outcome POVMs and two-state preparations, the protocol retains full performance with probability one. We experimentally demonstrate the protocol on an optical platform, reliably distinguishing between several strategies. Our results provide a strong and robust tool for causal inference in quantum networks.