Ensemble Engineering to Overcome Destructive Cancellation in Quantum Measurements

arXiv:2605.03729v4 Announce Type: replace Abstract: Quantum state preparation can shape how positive and negative contributions combine in correlation measurements, providing a route to control cancellation through ensemble engineering. We develop a framework for relating this control to the prepared distribution, using the infinite-temperature trace of the same operator product as a uniform-weight reference for ensemble-dependent correlators. For diagonal observables, resolving both projector sectors separates each sector's probability mass from its conditional sign alignment and determines their contributions to the full correlator. A worked example shows what a selected-sector description can miss, and a simple bound limits the error from omitting the complementary contribution. We use two complementary preparations: Grover-type amplitude amplification to redistribute probability toward a specified target, and oracle-free shallow circuits to shape the distribution at low depth. Zero-time benchmarks combine noiseless simulations with finite-shot sampling and IBM Quantum demonstrations on up to 20 qubits. Sector statistics distinguish low occupation from cancellation within an occupied sector, while comparisons with noiseless simulations show that characteristic features of the engineered cumulative patterns persist on hardware. We also extend the analysis to multi-qubit diagonal observables and connect their sign and sector rules to explicit preparation choices. These results provide a basis for designing and assessing structured ensembles through their operator-resolved contributions to quantum correlation measurements.