Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental noisy multiparameter quantum bounds   Quantum multiparameter estimation involves estimating multiple parameters
simultaneously and can be more precise than estimating them individually. Our
interest here is to determine fundamental quantum limits to the achievable
multiparameter estimation precision in the presence of noise. We present a
lower bound to the estimation error covariance for a noisy initial probe state
evolving via a noiseless quantum channel. We then present a lower bound to the
estimation error covariance in the most general form for a noisy initial probe
state evolving via a noisy quantum channel. We show conditions and accordingly
measurements to attain these estimation precision limits for noisy systems. We
see that the Heisenberg precision scaling of $1/N$ can be achieved with a probe
comprising $N$ particles even in the presence of noise. In fact, some noise in
the initial probe state or the quantum channel can serve as a feature rather
than a bug, since the estimation precision scaling achievable in the presence
of noise in the initial state or the channel in some situations is impossible
in the absence of noise in the initial state or the channel. However, a lot of
noise harms the quantum advantage achievable with $N$ parallel resources, and
allows for a best precision scaling of $1/\sqrt{N}$. Moreover, the Heisenberg
precision limit can be beaten with noise in the channel, and we present a
super-Heisenberg precision limit with scaling of $1/N^2$ for optimal amount of
noise in the channel, characterized by one-particle evolution operators.
Further, using $\gamma$-particle evolution operators for the noisy channel,
where $\gamma>1$, the best precision scaling attainable is $1/N^{2\gamma}$,
which is otherwise known to be only possible using $2\gamma$-particle evolution
operators for a noiseless channel.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph