The uncertainty relation for joint measurement of position and momentum

@article{Werner2004TheUR,
  title={The uncertainty relation for joint measurement of position and momentum},
  author={Reinhard F. Werner},
  journal={Quantum Information & Computation},
  year={2004},
  volume={4},
  pages={546-562}
}
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form (∆P )(∆Q) ≥ C~, 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 ∆Q of the position measurement, and the perturbation ∆P of the conjugate variable introduced by… CONTINUE READING
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