Generalized uncertainty relations: Theory, examples, and Lorentz invariance

@article{Braunstein1996GeneralizedUR,
  title={Generalized uncertainty relations: Theory, examples, and Lorentz invariance},
  author={Samuel L. Braunstein and Carlton M. Caves and Gerard J. Milburn},
  journal={Annals of Physics},
  year={1996},
  volume={247},
  pages={135-173}
}
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter - e.g., elapsed time - may be determined via arbitrary data analysis of arbitrary measurements on N identically prepared quantum systems. The limits are… 

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