Fundamental limits to contrast reversal of self-fidelity correlations

Abstract: In measurement design, it is common to engineer anti-contrast readouts -- two measurements that respond as differently as possible to the same inputs so that common-mode contributions are suppressed. To assess the fundamental scope of this strategy in unitary dynamics, we ask whether two evolutions can be made uniformly opposite over a broad input ensemble, or whether quantum mechanics imposes a structural limit on such opposition. We address this by treating self-fidelity (survival probability) as a random variable on projective state space and adopting the Pearson correlation coefficient as a device-agnostic measure of global opposition between two evolutions. Within this framework we establish the following theorem: For any nontrivial pair of unitaries, self-fidelity maps cannot be point-wise complementary correlation on the entire state space. Consequently, the mathematical lower edge of the correlation bound is not physically attainable, which we interpret as a unitary-geometric floor on anti-contrast, independent of hardware specifics and noise models. We make this floor explicit in realizable settings. In a single-qubit Bloch-sphere Ramsey model, a closed-form relation shows that a residual common-mode component persists even under nominally optimal tuning. In higher dimensions, Haar/design moment identities reduce ensemble means and covariances of self-fidelity to a small set of unitary invariants, yielding the same conclusion irrespective of implementation details. Taken together, these results provide a model-independent criterion for what anti-contrast can and cannot achieve in unitary sensing protocols.