Feedback control of quantum dynamical systems and applications in metrology

Project description

The ability to manipulate, control and measure quantum systems is a central issue in Quantum Technology applications such as quantum computation, cryptography, and high precision metrology [1]. Most realistic systems interact with an environment and it is important to understand how this affects the performance of quantum protocols and how it can be used to improve it. The input-output theory of quantum open systems [2] offers a clear conceptual understanding of quantum dynamical systems and continuous-time measurements, and has been used extensively at interpreting experimental data in quantum optics. Mathematically, we deal with an extension of the classical filtering theory used in control engineering at estimating an unobservable signal of interest from some available noisy data [3].

This projects aims at investigating the identification and control of quantum dynamical systems in the framework of the input-output formalism. As an example, consider a quantum system (atom) interacting with an incoming "quantum noise" (electromagnetic field); the output fields (emitted photons) emerging from the interaction can be measured, in order to learn about the system's dynamical parameters (e.g. its hamiltonian). The goal is to find optimal system identification strategies which may involve input state preparation, output measurement design, and quantum feedback control. An interesting related question is to understand the information-disturbance trade-off which in the context of quantum dynamical systems becomes identification-control trade-off.

The first steps in this direction were made in [4] which introduce the concept of asymptotic quantum Fisher information for "non-linear" quantum Markov processes, and [5] which investigates system identification for linear quantum systems, using transfer functions techniques from control theory. A furhter goal is to develop genearal Central Limit theory for quantum output processes as a probablistic underpinning of the asymptotic estimation theory. Another direction is the recently found connection between dynamical phase transitions in many-body open systems and high precision metrology for dynamical parameters (see arXiv:1411.3914).