From the noncommutative nature of quantum mechanics, estimation of canonical observables q and p is essentially restricted in its performance by the Heisenberg uncertainty relation, Δ q 2 Δ p 2 ≥ 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 η (0,1]. It is then clarified that the above Heisenberg uncertainty relation is replaced by Δ q 2 Δ p 2 ≥ 2 4η if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - 2007 Sep 19|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics