858 research outputs found
On Haag Duality for Pure States of Quantum Spin Chain
We consider quantum spin chains and their translationally invariant pure
states. We prove Haag duality for quasilocal observables localized in
semi-infinite intervals when the von Neumann algebras generated by observables
localized in these intervals are not type I
Uncertainty Relations for Joint Localizability and Joint Measurability in Finite-Dimensional Systems
Two quantities quantifying uncertainty relations are examined. In
J.Math.Phys. 48, 082103 (2007), Busch and Pearson investigated the limitation
on joint localizability and joint measurement of position and momentum by
introducing overall width and error bar width. In this paper, we show a simple
relationship between these quantities for finite-dimensional systems. Our
result indicates that if there is a bound on joint localizability, it is
possible to obtain a similar bound on joint measurability. For
finite-dimensional systems, uncertainty relations for a pair of general
projection-valued measures are obtained as by-products.Comment: 10 pages. To appear in Journal of Mathematical Physic
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