Heisenberg’s uncertainty principle for simultaneous measurement of positive-operator-valued measures
Takayuki Miyadera, Hideki Imai
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.
arXiv:0809.1714•Physical Review A•Nov 24, 2008•36 citations