Individual-case conservation under full analysis of quantum experiments

Prove that for any quantum experiment testing conservation laws (e.g., energy, linear momentum, or angular momentum), a complete analysis that explicitly models the state-preparation process (including entanglement with the preparation device used as a reference frame) and the measurement interaction with post-selection ensures that conservation is obeyed in every individual run, not only at the statistical (ensemble) level.

Background

The paper revisits cases where standard statistical conservation in quantum mechanics holds, yet specific individual runs appear to violate conservation, notably via superoscillation-based scenarios where a particle emerges with a conserved quantity (such as angular momentum) exceeding any component present in its prepared state while the measurement device does not supply the difference. The authors show that when the preparation stage and reference frames are explicitly modeled, an entangled preparer–particle state leads to a time-holistic double non-conservation that compensates to restore overall conservation in those individual cases.

Motivated by this resolution in an angular momentum setting, the authors propose a general conjecture: whenever the full preparation, reference-frame, and measurement dynamics are accounted for, conservation should hold in individual cases across conservation experiments, not merely statistically. Establishing this assertion would require demonstrating its validity beyond the specific superoscillatory constructions analyzed in the paper.