arXiv:quant-ph/0405184 · Quantum Information and Computation

The uncertainty relation for joint measurement of position and momentum

Reinhard F. Werner

Published Dec 1, 2004• 59 citations

Abstract

We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form (\Delta P)(\Delta Q)\geq C\hbar, where the `uncertainties' quantify the difference between the marginals of the joint measurement and the corresponding ideal observable. Applied to an approximate position measurement followed by a momentum measurement, the uncertainties become the precision \Delta Q of the position measurement, and the perturbation \Delta P of the conjugate variable introduced by such a measurement. We also determine the best constant C, which is attained for a unique phase space covariant measurement.

DOI: 10.26421/qic4.6-7-13

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