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arXiv · 0809.1714

Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

Takayuki Miyadera·Hideki Imai
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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.

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Takayuki Miyadera, Hideki Imai. 2008-11-22. Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures. https://doi.org/10.1103/physreva.78.052119

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