Information geometry under hierarchical quantum measurement
- URL: http://arxiv.org/abs/2206.13095v1
- Date: Mon, 27 Jun 2022 07:58:41 GMT
- Title: Information geometry under hierarchical quantum measurement
- Authors: Hongzhen Chen, Yu Chen, Haidong Yuan
- Abstract summary: In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information.
Here we analyze the discrepancy in terms of the Fisher information metric and present a framework that can provide analytical bounds on the difference under hierarchical quantum measurements.
- Score: 4.980960723762946
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In most quantum technologies, measurements need to be performed on the
parametrized quantum states to transform the quantum information to classical
information. The measurements, however, inevitably distort the information. The
characterization of the discrepancy is an important subject in quantum
information science, which plays a key role in understanding the difference
between the structures of the quantum and classical information. Here we
analyze the discrepancy in terms of the Fisher information metric and present a
framework that can provide analytical bounds on the difference under
hierarchical quantum measurements. Specifically, we present a set of analytical
bounds on the difference between the quantum and classical Fisher information
metric under hierarchical p-local quantum measurements, which are measurements
that can be performed collectively on at most p copies of quantum states. The
results can be directly transformed to the precision limit in multi-parameter
quantum metrology, which leads to characterizations of the tradeoff among the
precision of different parameters. The framework also provides a coherent
picture for various existing results by including them as special cases.
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