Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Fisher information matrix for unitary processes: closed relation
  for $SU(2)$   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 $SU(2)$
processes for an arbitrary number of estimation parameters and an 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
parametrization. We illustrate our results by obtaining the quantum Fisher
information matrix of the so-called angle-axis parameters of a general $SU(2)$
process. 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 parametrization to the one of the other
parametrization. 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.

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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con