Quantum Fisher Information And Its Application In Optical Phase Estimate

In recent years, the precise measurement technology based on the quantum interferometer has achieved rapid development. How to utilize the quantum interferometer to obtain high precision measurement is one of the basis subjects in a series of fields, such as weak magnetic field detection, gravitational wave detection and atomic clocks, etc. Quantum Fisher information (QFI) can be used to study the quantum measurement precision, due to it gives the ultimate limit of the accuracy in the parameter estimation. In this paper, using the Mach-Zehnder interferometer (MZI), we have carried out a series of work basing on the QFI. The main innovative results are as follows:1. Basing on the previous works, we develop the general expression of the quantum fisher information. In the Hilbert space, using the completeness of the reduced density-matrix eigenstates, we rederive the expression of the quantum Fisher information and split it into three terms. The first term is the classical Fisher information for the probability distribution. The second term is a weighted average over the quantum Fisher information for each pure state. The last term is a correction term, reducing the QFI and hence the estimation precision below the pure-state case. Compared with previous general expression of QFI for the mixed states, our expression has two advantages. First, every term of the new expression has a clear physical meaning, which is advantageous for the theoretical analysis. In addition, the new form of expression is relatively simple. It avoids complex calculations, which make us easy to get the accurate results. Up to now, our expression has been obtained much attentions and references at home and abroad.2. Considering a two-mode squeezed vacuum state as the input of the Mach-Zehnder interferometer, we analyze the phase sensitivities for the parity measurement and the Sz2 measurement. The results show that both the measurements can achieve the quantum Carmer-Rao bound. For parity measurement, the optimal phase is at π/2; while for the Sz2 measurement, it is at phase origin. For this case, the Sz2measurement is more advantageous to measure small phase shift. When the phase has a deviation from the phase origin, the change of the phase sensitivity for the Sz2 measurement is relatively slow, which is more advantageous to get higher accuracy measurement.3. An exact analytical expression of quantum Fisher information of entangled coherent state is derived to show the role of photon losses on the ultimate phase sensitivity. The loss-induced quantum decoherence leads to a transition of the estimation precision from the Heisenberg scaling to the classical scaling as the number of lost photons Rn increases, where R is the photon loss rate and n is the mean photon number of the initial ECS. This behavior is in sharp contrast to the NOON state, for which the photon losses eliminate completely the phase information stored in the coherence part of the reduced density matrix. The ultimate precision of the NOON state gets even worse than the classical limit when Rn(?)1. Surprisingly, we find that the precision of the NOON state may be better than that of the ECS within the crossover region Rn-1. This is because although the classical term of the ECS is robust against the photon losses, the Heisenberg term decays about twice as quickly as that of the NOON state.