FEEDBACK CONTROL OF QUANTUM SYSTEMS

J. W. Clark, Dennis G. Lucarelli, Tzyh‐Jong Tarn

S. G. Schirmer, A. I. Solomon

Howard M. Wiseman

Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

Daoyi Dong, Zonghai Chen, Chenbin Zhang +1 more

P. Zoller, J. I. Cirac, S. M. Girvin +1 more

V. P. Belavkin

Abstract. The fundamental mathematical definitions of the controlled feedback Markov dynamics of quantum-mechanical systems are introduced with regard to the dynamical reduction and filtering of quantum states in the course of quantum measurement in either discrete or continuous real time. The concept of sufficient coordinates for the description of a posteriori quantum states in a given class is introduced and it is proved that they form a classical Markov process with values in either state operators or state vector space. The general problem of optimal control of a quantum-mechanical system is discussed and the corresponding Bellman equation in the space of sufficient coordinates is derived. The results are illustrated in the example of control of the semigroup dynamics of a quantum system that is instantaneously observed at discrete times and evolves between measurement times according to the Schrődinger equation. 1.