Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

Naoki Yamamoto, Shinji Hara

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number034102
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume76
Issue number3
DOIs
Publication statusPublished - 2007 Sep 19
Externally publishedYes

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quantum mechanics

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

Cite this

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