Theoretical Study On Quantum Fisher Information For Witnessing Multipartite Entanglement

As the unique property of quantum mechanics,quantum entanglement describes the quantum correlations between subsystems,and plays a crucial role in quantum precision measurement,quantum information,quantum computation and next-generation quantum techonology.With the advanced progress of experimental methods in controlling laser and trapping atoms and ions,an extensively research about quantum entanglement,especially for multipartite entanglement is explored,such as the access to entanglement,the entanglement detection,the coherent operation,etc.Developing a criterion for witnessing multipartite entanglement is one of the hot topics in this field,especially for the measurement-independent and experiment-friendly ones.It is Italian scientists,Augusto Smerzi and Luca Pezzè,who firstly pointed out that Quantum Fisher information is a good quantity to play this role,from the point of insight on the statistical nature of quantum states.Underwent the quantum perturbing or a unitary operation,the statistical response(statistical speed)of a quantum state performs quite different behaviors and the entangled state has a faster statistical response than the separable state,that is,a larger Quantum Fisher information.Starting from this point,we have finished the following works: extending the original ideas of A.Smerzi in 2009 to the non-local unitary operation,and showing that Quantum Fisher information can still be a criterion for witnessing multipartite entanglement even involving nonlocal operation;considering the relationship between Quantum Fisher information and quantum parameter estimation,Shot Noise and Heisenberg limit are presented within the Ising-like model;higher-order fitting method is proposed to directly extract Fisher information from experimental data;the effect of statistical methods on Fisher information is investigated.The details are in the following.Firstly,as shown in 2009,Quantum Fisher information is proportional to the statistical speed of a quantum state to the unitary linear operation.Since that the entangled state has faster statistical speed than the separable one,Quantum Fisher information can be used as one kind of criteria for witnessing multipartite entanglement.After the calculation of the Quantum Fisher information under the non-local unitary operation,we find a monotonous relationship between Quantum Fisher information and the strength of the non-local interaction.Therefore,Quantum Fisher information can be a good criterion.It is impossible or harder to avoid the non-local interactions between atoms or ions in real experiments,and so our work will be a good contribution in this field.Secondly,from the view of quantum estimation theory,Quantum Fisher information is inversed with the precision limit,as shown in Cramer-Rao theory.Based on the calculation of Quantum Fisher information under non-local unitary(Ising-like Hamiltonian)operation,we find that the non-local interaction may dramatically increase the precision limit.In this chapter,we have calculated the Shot Noise and Heisenberg limit under different fields,and have shown the explict forms of the corresponding optimal multipartite quantum states.Thirdly,due to the close relation between Quantum Fisher information and statistical speed of quantum states,the value of Quantum Fisher information can be directly extracted from the bare experimental data.Within a dichotomic measurement model,we make a throughtful investigation on two general methods for Quantum Fisher information,Hellinger distance and Kullback-Leibler entropy.The higher-order fitting method is suggested to obtain accurate Quantum Fisher information.Furthermore,the effect of two methods for Quantum Fisher information is shown by the analysis on recent experimental data.Finally,whether or not there exists a lowest bound for quantum parameter estimation is one of the open questions,especially in the finite experimental times.In this part,the quantum frequentist and Bayesian estimation are used to investigate various lowest bounds.We find that the two statistical methods can not be equal in most situations,since the quite different assumption of the two statistical theories.