Quantum Fisher Information In Interferometers

Quantum metrology,as a subject about quantum measurement and quantum statis-tical inference,has received extensive attention in recent years.Some related scientific technology and theoretical studies have developed rapidly.Quantum Fisher informa-tion,which corresponds to classic Fisher information,is a core concept in quantum metrology.Quantum Fisher information can be used to quantitatively describe the measurement precision of the parameter to be estimated.This paper mainly studies the quantum Fisher information in the interferometer:the quantum Fisher information is used to measure the measurement precision of the parameter to be estimated,and the initial state is selected according to the obtained analytical results to optimize the phase sensitivity of the interferometer.The main content of this thesis is arranged as follows:In Chapter 2,we review the theoretical knowledge of classical Fisher information and quantum Fisher information.For quantum Fisher information,we review three different methods,and elaborate on the spectral decomposition method that we will use later and its simplified form in the case of unitary parameterization.In Chapter 3,we mainly introduce the two-mode interferometer described by su(2)and su(1,1)two algebras.Starting from Schrodinger's representation,we review the algebraic representation of both su(2)and su(1,1)interferometers.In Chapter 4,we introduce a commutator operator function method,which can be used to calculate infinite-order nested commutator superoperators.We use this method to analytically calculate the quantum Fisher information in the unitary parameterization process described by any finite-dimensional Lie algebra.We use su(2),su(1,1)and su(3)three algebras as examples to illustrate the universality of our calculation method.Then,the initial state is optimized according to the obtained quantum Fisher information to improve the measurement sensitivity of the interferometer.In Chapter 5,we consider how to allocate the average number of photons between the two input ports to optimize the phase sensitivity of the two-mode interferometer when the total average photon number of the two input ports is given.In both the su(2)and su(1,1)interferometers with a product of coherent and Fock states as inputs,we find there exists a critical value for the total photon number,below which the optimal phase sensitivity can be achieved with the second port being the vacuum state.We derive the analytical form of this critical value.Further,we consider a more general initial input state as a product state of coherent state and the squeezed Fock state.We can analytically divide the parameter space into three parts similar to a phase diagram,and find that critical phenomena occur in two regions.In Chapter 6,in order to enhance the phase sensitivity of the Mach-Zehnder in-terferometer,we add an tunable phase shift operation before the input light enters the interferometer.The analytical result of the optimal phase shift is obtained,which on-ly depends on the initial input states.For a non-zero optimal phase shift,the phase sensitivity of the interferometers in the output ports can always be improved.We can achieve this enhancement for most states,including entangled and mixed states.We give three examples to illustrate how to obtain the optimal tunable phase.Compared with the previous existing methods,our scheme provides a general method to enhance the phase sensitivity,and it is easy to implement in experiments.In the appendix,we introduce the related derivations and basic knowledge,in-cluding the detail of the commutator operator function method,related information of several Lie algebras,and the detailed derivation of the formulas used in the two-mode interferometers.