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

We theoretically propose a cyclic quantum engine where a single-qubit working medium undergoes finite-time unitary strokes with adjustable duration, 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 τ_dr, which governs nonadiabatic transitions and phase accumulation, and the measurement parameter θ, which sets outcome probabilities and the magnitude of measurement-induced energy injection. Feedback acts solely through pulses, without altering stroke times. Including measurement and erasure costs, we show that coordinated tuning of τ_dr and θ yields substantial, robust gains in power and efficiency.