A fundamental lower bound of the cost for bit reset

A general measurement process, involving a unitary operation on the composite system and a projective measurement on one of the subsystems, is proposed. The average entropy change of the composite system due to the measurement induced irreversibility is evaluated and found to be positive by applying the quantum-trajectory approach. This leads to an inequality associated with the fundamental lower bound on the thermodynamic energy cost for information erasure. We show that the lower bound is determined by the cost for erasing information and the relative entropy. A two-spin system is adopted to verify the validity of the findings. The results provide a deeper understanding of the performance of measurement and control systems.