  The tradeoff relation between speed and cost is a central issue in designing
fast and efficient information processing devices. We derive an achievable
bound on thermodynamic cost for obtaining information through finite-time
(non-quasi-static) measurements. Our proof is based on optimal transport
theory, which enables us to identify the explicit protocol to achieve the
obtained bound. Moreover, we demonstrate that the optimal protocol can be
approximately implemented by an experimentally feasible setup with quantum
dots. Our results would lead to design principles of high-speed and
low-energy-cost information processing.
