Quantum Limits of Measurements and Uncertainty Principle
arXiv:1505.05083 · doi:10.1007/3-540-53862-3_161
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.
15 pages, presented at the International Workshop on Quantum Aspects of Optical Communications, C.N.R.S. Paris, France, November 26-28, 1990