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

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

2008-09-10

arxiv.org/abs/0809.1714v3

Phys. Rev. A 78, 052119 (2008)

Physics

Quantum Physics

7 pages, 1 figure. To appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.78.052119

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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