https://doi.org/10.1140/epjp/s13360-024-05011-7
Regular Article
Characterizing stabilizer states and H-type magic states via uncertainty relations
1
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China
2
School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
Received:
13
December
2023
Accepted:
15
February
2024
Published online:
7
March
2024
Although the conventional Heisenberg uncertainty relations have been extensively studied, there are still many interesting features related to uncertainty awaiting for exploring. In this work, we introduce the notion of renormalized uncertainty and study its implications and applications. We analytically characterize the minimum and maximum uncertainty states for some basic uncertainty relations in qubit systems. We further introduce a symmetric version of renormalized uncertainty and employ it to characterize some important states in the stabilizer formalism of quantum computation. We prove that the minimum uncertainty states are precisely the stabilizer states, while the maximum uncertainty states are precisely the H-type magic states. We connect the minimum and maximum uncertainty states via the T-gates, which are fundamental and crucial quantum gates enabling universal quantum computation. These results reveal certain features of stabilizer states, magic states, and T-gates from the perspective of uncertainty.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
