Uncertainty regions of observables and state-independent uncertainty relations

The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via dete...

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Bibliographic Details
Published in:Quantum information processing 2021-11, Vol.20 (11), Article 357
Main Authors: Zhang, Lin, Luo, Shunlong, Fei, Shao-Ming, Wu, Junde
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Deviation
Entanglement
Lower bounds
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Uncertainty
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Summary:The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03303-w