Quantum Control: Theory and Measurement

Daoyi Dong

Quantum control theory is a new interdiscipline, which mainly studies the control of quantum states for systems in the microworld. First, quantum control theory is elicited through quantum information theory. Then the research contents and characteristics of quantum control theory and measurement theory in quantum control are expounded. Current research of quantum control theory is also summarized. And last, advanced research on quantum control theory is proposed.

H. Ezawa, Yoshimasa Murayama

Maison Clouâtré

Quantum control plays a crucial role in quantum inference tasks such as parameter estimation and state discrimination. Despite this, the fields of quantum control and quantum inference have remained largely disjoint. We bridge these fields, revealing that (i) quantum control determines the fundamental performance limits of quantum estimation and state discrimination, and (ii) control of statistical information measures enables performance approaching these limits. This thesis begins by establishing an axiomatic formalization of quantum control theory and developing a mathematical framework for analyzing, approximating, and controlling the evolution of quantum systems. A self-contained treatment of optimal quantum control is presented. This treatment exploits the unique structure of quantum dynamics rather than merely borrowing notions from classical control. Quantum control systems are shown to be universally contractive, which plays an important role in the treatment of optimal quantum control and in the derivation of various approximation results. Next, the thesis proceeds by addressing statistical inference problems, with emphasis on parameter estimation and state discrimination. Controlled information measures are introduced, providing more sensible alternatives to existing information measures for quantum inference, e.g., quantum Fisher information. Controlled information measures are shown to exhibit useful properties, e.g., data-processing inequalities. Methods for deriving achievability and converse bounds on controlled information measures are developed, and adaptive control techniques for information maximization are proposed. This thesis leverages a cross-pollination of control theory, statistical inference, and quantum information towards the development of an application-focused theory of quantum inference.

Gerard J Milburn

WU Guo-li

The quantum control theory based on the quantum mechenics and quantum information theory is rising.Quantum control is rather different from classical control.It gives us the new philosophical meanings:wave-function is the unification of quantum reality and quantum information,quantum state is the unification of measurability and controllability,and quantum state is an important resources.

H. Ezawa