Abstract
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator . Utilizing this representation, quantum Fisher information is only determined by and the initial state. Furthermore, can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of . For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
Highlights
Quantum Fisher information is a central quantity in quantum metrology
We discuss an alternative representation of quantum Fisher information for unitary parametrization processes
Some of them can even approach to the Heisenberg limit, a limit given by the quantum mechanics, showing the power of quantum metrology
Summary
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The counterpart of quantumÀFisÈher infÉoÁrmation is called quantum Fisher information matrix F , of which the element is defined as F ab~Tr r La,Lb , where La, Lb are the SLD operators for parameters a and b, respectively It has been found[27] that quantum Fisher information can be expressed in an alternative representation, that all information of parametrization process in quantum Fisher information is involved in a Hermitian operator H. All optimal states to access maximum quantum Fisher information are found in this system Considering this spin-half system as a multiparameter system, the quantum Fisher information matrix, can be obtained by the known form of H in single parameter estimations. The maximum quantum Fisher information and the optimal condition are discussed
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