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

Abstract

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.