Theoretical Limits of Protocols for Distinguishing Different Unravelings

TL;DR

This paper proves that different stochastic unravelings of quantum master equations cannot be distinguished operationally without prior knowledge, and such attempts would violate causality.

Contribution

It establishes the fundamental impossibility of distinguishing quantum unravelings operationally and links this to causality constraints in quantum theory.

Findings

Nonlinear quantities depend on the unraveling and cannot be accessed without prior knowledge.

Operational distinguishability of unravelings is fundamentally unfeasible.

Distinguishing unravelings without prior info would enable superluminal signaling.

Abstract

Stochastic unravelings of Lindblad-type master equations, such as stochastic Schr\"odinger equations (SSEs), 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.