Thermodynamically Optimal Information Gain in Finite Time Measurement*

Elucidating the fundamental energy cost for measurement process is one of the central topics in thermodynamics and the fundamantal bound on the energy cost has been clarified by the development of information thermodynamics. While the bound can be achieved in quasi-static processes, the energy cost for measurement process achieved in finite time, which is important from the viewpoint of application, has yet to be fully clarified. 

In this talk, I will show the finite-time enegy cost for measurement process by incorporating optimal transport theory, which has attracted attention as a theory that provides tight bounds on the energy cost required for finite-time processes. First, we derive the upper bound on the mutual information that can be obtained under a given optimal transport distance. This is the most mathematically nontrivial part of this presentation. I will then explain that, by considering the dual problem, this upper bound gives the fundamental bound on the thermodynamic cost required to obtain information in finite-time measurement. This bound is tight, and we can also identify the optimal protocol to achieve it. Moreover, I will explain that, in an experimentally feasible setting with quantum dots, the optimal protocol can be approximately implemented. This result is expected to lead to design principles for high-speed and low-energy-cost information processes.