Measurement-Conditioned Coherent Control: Driving-Speed and Measurement-Basis Optimization in Quantum Heat Engines

We theoretically propose a cyclic quantum engine in which a single-qubit working medium undergoes finitetime unitary strokes with adjustable durations, followed by a projective measurement and an outcome-dependent coherent pulse (π or π/2 rotation). The protocol separates two independent control handles: the unitary driving speed τdr, which governs nonadiabatic transitions and phase accumulation, and the measurement parameter θ, which sets the outcome probabilities and the magnitude of measurement-induced energy injection. Feedback functions solely through pulses without altering the stroke time. Including the measurement and erasure costs, we show that the coordinated tuning of τdr and θ yields substantial and robust gains in terms of power and efficiency.