State is a mathematical description of the physical system that provides past and future information for this system. Leohart once made a standard statement on state (Raymer and Beck, 2004): "Knowing the state means knowing the maximally available statistical information about all physical quantities of a physical object." The technique of state estimation is a method, that can obtain a system's true state as far as possible by measurement. In essence, quantum state estimation and the corresponding classical state estimation mainly differ in three points. First of all, the state of a classical system usually has a clear physical significance, which is a real physical quantity of the system. The direct measurement of this physical quantity can usually give the corresponding state value in the permitted condition, but the state of a quantum system-wave function or a density operator is not a real physical quantity. It cannot acquire a certain value of a quantum state by direct state measurement. However, one can deduce the state with the aid of measurement of some observable quantities of the quantum system. Second, a classical system is determinism in theory. If the system is input by a signal, the state of the system at any time will be perfectly determined by the initial state. When the system suffers the impact of the disturbance, the instantaneous state of the system will have all kinds of noise. With the aid of the corresponding estimation technique, one can deal with the system noise and obtain the real state as far as possible. In contrast, in essence a quantum system is ruled by probability theory. Even though the quantum system does not suffer the consequence of any interference, one can only acquire a random result from the measurement of the quantum system. What is more, if the quantum system is disturbed, in order to obtain the state, additional handling of the relevant noise is needed. Third, as regards the method of realization of the measurement, the measurement of the classical system does not result in substantial damage to the system so in principle this system can be measured many times. Nevertheless, a quantum system is very fragile and the measurement usually will cause substantial damage, which the same quantum system from being reused to make multiple measurements.Classical state estimation methods is are more developed than state estimation methods in quantum systems. In reality, most state estimation methods are aimed at the reconstruction of Control of Quantum Systems: Theory and Methods, First Edition. Shuang Cong.