Theoretical limits of protocols for distinguishing different unravelings

Stochastic unravelings of Lindblad-type master equations, such as stochastic Schrödinger equations, provide powerful tools to model open quantum systems and continuous measurement processes. The same master equation can be unraveled in different ways; while these unravelings differ at the level of quantum trajectories, by construction they all yield the same averaged dynamics for the density operator. A recent question of both foundational and practical relevance is whether such unravelings can be operationally distinguished, given that certain nonlinear quantities—such as covariances and higher-order moments of conditional expectation values—are unraveling dependent. We show that these quantities cannot be accessed unless the measurement scheme (i.e., the unraveling) is known in advance. This renders any operational protocol to distinguish unravelings fundamentally unfeasible. We further establish that assuming access to such nonlinear quantities without prior knowledge of the unraveling would enable superluminal signaling, violating relativistic causality.