### 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 language | English |
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Article number | 034102 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 76 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Sep 19 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

**Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement.** / Yamamoto, Naoki; Hara, Shinji.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

AU - Yamamoto, Naoki

AU - Hara, Shinji

PY - 2007/9/19

Y1 - 2007/9/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34548852860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548852860&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.76.034102

DO - 10.1103/PhysRevA.76.034102

M3 - Article

AN - SCOPUS:34548852860

VL - 76

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 034102

ER -