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arXiv · 1505.05083

Quantum Limits of Measurements and Uncertainty Principle

Masanao Ozawa
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Abstract

In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square measurement errors arising in joint measurements of noncommuting observables is established. We give a rigorous condition for holding of the standard quantum limit (SQL) for repeated measurements, and prove that if a measuring instrument has no larger root-mean-square preparational error than the root-mean-square measurement errors then it obeys the SQL. As shown previously, we can even construct many linear models of position measurement which circumvent this condition for the SQL.

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Masanao Ozawa. 2015-05-19. Quantum Limits of Measurements and Uncertainty Principle. https://doi.org/10.1007/3-540-53862-3_161

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