Reviews of Uncertainty Relations

  • Yu Watanabe
Part of the Springer Theses book series (Springer Theses)


In this chapter, we provide a brief overview of various uncertainty relations. First, we review historical uncertainty relations: Heisenberg’s gamma-ray microscope and von-Neumann’s Doppler speed meter. These uncertainty relations epitomize trade-off relation between error and disturbance in quantum measurement process. Next, we review a different type of uncertainty relations: Kennard-Robertson’s inequality and Schrödinger’s inequality. These characterize trade-off relations of inherent fluctuations of observables. Finally, we review Arthurs-Goodman’s inequality and Ozawa’s inequality that based on modern quantum measurement theory.


Commutation Relation Measurement Process Uncertainty Relation Quantum Measurement Projective Measurement 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Kyoto UniversityKyotoJapan

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