Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal condition for measurement observable via error-propagation   Propagation of error is a widely used estimation tool in experiments, where
the estimation precision of the parameter depends on the fluctuation of the
physical observable. Thus which observable is chosen will greatly affect the
estimation sensitivity. Here we study the optimal observable for the ultimate
sensitivity bounded by the quantum Cram\'er-Rao theorem in parameter
estimation. By invoking the Schr\"odinger-Robertson uncertainty relation, we
derive the necessary and sufficient condition for the optimal observables
saturating the ultimate sensitivity for single parameter estimate. By applying
this condition to Greenberg-Horne-Zeilinger states, we obtain the general
expression of the optimal observable for separable measurements to achieve the
Heisenberg-limit precision and show that it is closely related to the parity
measurement. However, Jose {\em et al} [Phys. Rev. A {\bf 87}, 022330 (2013)]
have claimed that the Heisenberg limit may not be obtained via separable
measurements. We show this claim is incorrect.

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The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio