Measurement-Feedback Quantum Information Engine: Coherence-Transition Interference and Correlated Work Statistics

Measurement and feedback jointly prepare coherence and select finite-time dynamics in quantum information engines. Complementing a companion experimental realization, we develop a mechanism-resolved theory of the resulting work statistics and temporal correlations. The con?ditional work separates into population transfer and a phase-sensitive coherence-transition inter?ference term. Symmetric full counting statistics maps this interference to an equal-and-opposite half-quantum pair in the work quasiprobability, entering odd moments while leaving even moments fixed by endpoint mixing. An outcome-resolved tilted kernel then propagates these statistics through the correlated measurement record, yielding finite-cycle and fixed-time fluctuation corrections. The same memory reduces the reversible record-reset cost from the one-symbol entropy to the entropy rate. Our results link coherent work statistics, feedback memory, and information thermodynamics