TY - JOUR

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

AU - Yamamoto, Naoki

AU - Hara, Shinji

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

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.

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U2 - 10.1103/PhysRevA.76.034102

DO - 10.1103/PhysRevA.76.034102

M3 - Article

AN - SCOPUS:34548852860

SN - 1050-2947

VL - 76

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

M1 - 034102

ER -