International Iran Conferences on Quantum Information 2018 , 2018-09-08

#### Title : ( Quantum Fisher information for unitary processes )

Citation: BibTeX | EndNote

#### Abstract

Quantum Fisher information plays a central role in the field of quantum metrology. In this paper we study the problem of quantum Fisher information of unitary processes. Associated to each parameter $\theta_i$ of unitary process $U(\boldsymbol{\theta})$, there exists a unique Hermitian matrix $M_{\theta_i}=i(U^\dagger\partial_{\theta_i} U)$. Except for some simple cases, such as when the parameter under estimation is an overall multiplicative factor in the Hamiltonian, calculation of these matrices is not an easy task to treat even for estimating a single parameter of qubit systems. Using the Bloch vector $\boldsymbol{m}_{\theta_i}$, corresponding to each matrix $M_{\theta_i}$, we find a closed relation for the quantum Fisher information matrix of the qubit systems for an arbitrary number of estimation parameters and arbitrary initial state. We extend our results and present an explicit relation for each vector $\boldsymbol{m}_{\theta_i}$ for a general Hamiltonian with arbitrary parameterization. We illustrate our results by obtaining the quantum Fisher matrix of the so-called angle-axis parameters of a general $SU(2)$ Hamiltonian. Using a linear transformation between two different parameter spaces of a unitary process, we provide a way to move from quantum Fisher information of a unitary process in a given parameterization to the one of the other parameterization. Knowing this linear transformation enables one to calculate the quantum Fisher information of a composite unitary process, i.e. a unitary process resulted from successive action of some simple unitary processes. We apply this method for a spin-half system and obtain the quantum Fisher matrix of the coset parameters in terms of the one of the angle-axis parameters.

#### Keywords

, Quantum Metrology, Quantum Fisher information, Unitary processes
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@inproceedings{paperid:1070098,
title = {Quantum Fisher information for unitary processes},
booktitle = {International Iran Conferences on Quantum Information 2018},
year = {2018},
location = {تهران, IRAN},
keywords = {Quantum Metrology; Quantum Fisher information; Unitary processes},
}