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Title: Near-optimal variance-based uncertainty relations
Authors: Xiao, Yunlong
Jing, Naihuan
Yu, Bing
Fei, Shao-Ming
Li-Jost, Xianqing
Keywords: Science::Physics
Issue Date: 2022
Source: Xiao, Y., Jing, N., Yu, B., Fei, S. & Li-Jost, X. (2022). Near-optimal variance-based uncertainty relations. Frontiers in Physics, 10, 846330-.
Project: NRF-NRFF2016-02
RG162/19 (S)
Journal: Frontiers in Physics 
Abstract: Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum theory. Aside from its fundamental significance, the mathematical characterization of this restriction, known as `uncertainty relation', plays important roles in a wide range of applications, stimulating the formation of tighter uncertainty relations. In this work, we investigate the fundamental limitations of variance-based uncertainty relations, and introduce several `near optimal' bounds for incompatible observables. Our results consist of two morphologically distinct phases: lower bounds that illustrate the uncertainties about measurement outcomes, and the upper bound that indicates the potential knowledge we can gain. Combining them together leads to an \emph{uncertainty interval}, which captures the essence of uncertainties in quantum theory. Finally, we have detailed how to formulate lower bounds for product-form variance-based uncertainty relations by employing entropic uncertainty relations, and hence built a link between different forms of uncertainty relations.
ISSN: 2296-424X
DOI: 10.3389/fphy.2022.846330
Schools: School of Physical and Mathematical Sciences 
Research Centres: Nanyang Quantum Hub
Rights: © 2022 Xiao, Jing, Yu, Fei and Li-Jost. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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