The uncertainty relation for joint measurement of position and momentum

Details The uncertainty relation for joint measurement of position and momentum The uncertainty relation for joint measurement of position and momentum

2004-05-30

arxiv.org/abs/quant-ph/0405184v1

Physics

Quantum Physics

17 pages, 4 figures; for Festschrift A.S. Holevo

Scientific paper

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.

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