Past quantum state estimation is a somewhat controversial topic in quantum physics. We have tackled this problem from a statistical estimation perspective.
Kentaro Ohki, "A smoothing theory for open quantum systems: The least mean square approach," Proceedings of 54th IEEE Conference on Decision and Control (CDC), pp. 4350-4355, 2015, arXiv
Comments: This paper implicitly establishes what weak values, introduced by Aharonov and coauthors, are, and proposes a recursive estimation of past quantum observables based on minimum mean square error estimation.
Kentaro Ohki "An invitation to quantum filtering and smoothing theory based on two inner products," RIMS Kokyuroku, No. 2018, pp. 18-44, 2017
Comments: This is a review article about quantum recursive estimation theory based on inner products over operator algebras.
Kentaro Ohki, "On recursive quantum state smoothing," Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, 2022
Comments: This paper investigates recursive quantum state smoothing. For general quantum smoothing problems, a quantum weak-valued state gives the minimum mean-square-error estimation. However, the weak-valued state is not a "physical" state, so this paper examines the conditions under which the past quantum state can be obtained.
Quantum feedback control is divided into two categories: coherent feedback and measurement-based feedback. We focus mainly on the latter. Measurement-based quantum feedback control is a type of nonlinear stochastic distributional control because the quantum state is a generalization of a probability distribution. This makes controller synthesis challenging.
Shoju Enami, Kentaro Ohki, "A proposal of adaptive parameter tuning for robust stabilizing control of N–level quantum angular momentum systems," Proceedings of the 2021 60th IEEE Conference on Decision and Control (CDC), pp. 2518-2524, 2021, arXiv
Comments: This paper proposes an adaptive control for a kind of uncertain quantum system. The proposed one works even when the nominal parameters are far from the true ones.
Weichao Liang, Kentaro Ohki, Francesco Ticozzi, "Exploring the Robustness of Stabilizing Controls for Stochastic Quantum Evolutions," SIAM Journal on Control and Optimization, Vol. 63, Iss. 1, 2025, arXiv
Comments: This paper investigates the effect of unmodeled dynamics on equilibrium in quantum systems and how stabilizing controllers keep the quantum state near equilibrium.