Extreme expected values and their applications in quantum information
processing
- URL: http://arxiv.org/abs/2111.00466v1
- Date: Sun, 31 Oct 2021 11:10:39 GMT
- Title: Extreme expected values and their applications in quantum information
processing
- Authors: Wangjun Lu, Lei Shao, Xingyu Zhang, Zhucheng Zhang, Jie Chen, Hong
Tao, and Xiaoguang Wang
- Abstract summary: We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value.
We apply the proved theory to solve three problems in quantum information processing.
- Score: 7.4733340808812505
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the probability distribution when the monotonic function $F(X)$
of the independent variable $X$ takes the maximum or minimum expected value
under the two constraints of a certain probability and a certain expected value
of the independent variable $X$. We proposed an equal probability and equal
expected value splitting method. With this method, we proved four inequalities,
and two of them can be reduced to Jensen's inequalities. Subsequently, we find
that after dividing the non-monotone function $H(X)$ into multiple monotone
intervals, the problem of solving the maximum and minimum expected values of
$H(X)$ can be transformed into the problem of solving the extreme value of a
multiple-variable function. Finally, we apply the proved theory to solve three
problems in quantum information processing. When studying the quantum parameter
estimation in Mach-Zehnder interferometer, for an equal total input photon
number, we find an optimal path-symmetric input state that makes the quantum
Fisher information take the maximum value, and we prove that the NOON state is
the path-symmetric state that makes the quantum Fisher information takes the
minimum value. When studying the quantum parameter estimation in
Landau-Zener-Jaynes-Cummings model, we find the optimal initial state of the
cavity field that makes the system obtain the maximum quantum Fisher
information. Finally, for an equal initial average photon number, we find the
optimal initial state of the cavity field that makes the Tavis-Cummings quantum
battery have the maximum stored energy and the maximum average charging power.
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