Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Standard Quantum Limit and Heisenberg Limit in Function Estimation   Unlike well-established parameter estimation, function estimation faces
conceptual and mathematical difficulties despite its enormous potential
utility. We establish the fundamental error bounds on function estimation in
quantum metrology for a spatially varying phase operator, where various degrees
of smooth functions are considered. The error bounds are identified in both
cases of absence and presence of interparticle entanglement, which correspond
to the standard quantum limit and the Heisenberg limit, respectively. Notably,
these error bounds can be reached by either position-localized states or
wavenumber-localized ones. In fact, we show that these error bounds are
theoretically optimal for any type of probe states, indicating that quantum
metrology on functions is also subject to the Nyquist-Shannon sampling theorem,
even if classical detection is replaced by quantum measurement.

21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs