Structural constraint on delayed-choice quantum eraser architectures

Delayed-choice quantum eraser (DCQE) experiments are often presented as challenging classical causal intuitions by correlating detection events with choices implemented at later times. While it is well understood that post-selection plays a crucial role in producing the observed interference patterns, the structural features underlying such correlations are rarely analyzed within a unified framework. In this work, we introduce a simple probabilistic constraint applicable to idealized DCQE architectures. We show that four intuitive properties -- statistical independence of the choice, absence of losses, deterministic routing conditioned on the choice, and distinct conditional detection distributions -- cannot be simultaneously satisfied. This incompatibility provides a transparent classification of DCQE schemes and clarifies how conditional interference patterns arise without invoking exotic mechanisms.