Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
Quantum Physics
2008-12-01 v3
Abstract
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive operator valued measures to be simultaneously measurable is obtained.
Keywords
Cite
@article{arxiv.0809.1714,
title = {Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures},
author = {Takayuki Miyadera and Hideki Imai},
journal= {arXiv preprint arXiv:0809.1714},
year = {2008}
}
Comments
7 pages, 1 figure. To appear in Phys. Rev. A