Physics – Quantum Physics
Scientific paper
2007-09-21
Physical Review A 76, 034102 (2007)
Physics
Quantum Physics
4 pages
Scientific paper
10.1103/PhysRevA.76.034102
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4$. This fundamental lower-bound may become bigger when taking the structure and quality of a specific measurement apparatus into account. In this paper, we consider a particle subjected to a linear dynamics that is continuously monitored with efficiency $\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty relation is replaced by $\mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4\eta$ if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.
Hara Shinji
Yamamoto Naoki
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