Fundamental limits to contrast reversal of survival probability 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 contributions that affect both readouts in the same way 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 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, survival probability 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 shared (channel-symmetric) component persists even under nominally optimal tuning. In higher dimensions, Haar/design moment identities reduce ensemble means and covariances of survival probability 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.