ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
Sum Types of Uncertainty Relations for Generalized Quasi-metric Adjusted Skew Informations
International Journal of Mathematical Analysis and Applications
Vol.5 , No. 4, Publication Date: Dec. 24, 2018, Page: 85-94
2298 Views Since December 24, 2018, 554 Downloads Since Dec. 24, 2018

Kenjiro Yanagi, Department of Mathematics, Josai University, Sakado, Japan.


It is well known that almost all uncertainty relations including Heisenberg uncertainty relation and Schr¨odinger uncertainty relation were given by product types of trace inequalities. This is why these results were proved by Schwarz’s inequality. These product types of uncertainty relations were extended to the case of not necessarily hermitian quantum mechanical observables and positive operators representing quantum states. On the other hand sum types of uncertainty relations were given for arbitrary finite N not necessarily hermitian quantum mechanical observables. Some uncertainty relations are presented by generalized quasi-metric adjusted skew informations for two different generalized states. These uncertainty relations are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Finally, the reverse inequalities of the sum types of uncertainty relations are obtained.


Trace Inequality, Metric Adjusted Skew Information, Generalized Quasi-metric Adjusted Skew Information


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