Characterization-free classification and identification of the environment between two quantum players
Identifying 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 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, under an explicit generic-sampling condition, a randomly selected binary measure-and-prepare setting retains exact-distribution identifiability with probability one. In the optical experiment, we use a reduced-randomness construction in which several preparation states are kept fixed. Nevertheless, the Markov-condition-based procedure yields the expected causal-order and memory-presence classification for every tested process realization and setting. This observation suggests that the randomization assumptions of the general theorem may be relaxed. Our results provide an operational framework for causal inference in quantum networks.