We study the disorder-perturbed transport of two entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass (e.g. two-particle N00N states) remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.
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