https://doi.org/10.1140/epjp/s13360-023-03873-x
Regular Article
Parameterized multi-observable sum uncertainty relations
1
School of Mathematical Sciences, Capital Normal University, 100048, Beijing, China
2
Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany
3
School of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, China
b
2190501022@cnu.edu.cn
c
feishm@cnu.edu.cn
Received:
7
November
2022
Accepted:
8
March
2023
Published online:
28
March
2023
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite N quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
