Uncertainty relations for noise and disturbance in generalized quantum measurements
Uncertainty relations for noise and disturbance in generalized quantum measurements
复制标题
DOI：
10.1016/j.aop.2003.12.012
复制
发表时间：
2004-06-01
影响因子：
3
通讯作者：
Ozawa, M
中科院分区：
文献类型：
--
作者：
Ozawa, M
海森伯格关于测量噪声和扰动的不确定度关系通常被理解为：在任何测量中，位置测量噪声和动量扰动的乘积不小于普朗克常数除以4PI。然而，在许多方面已经表明，在最一般的测量过程公式中，这种关系只适用于有限类别的测量仪器。本文将海森堡测不准关系推广到对所有可能的量子测量都成立的关系，由此得到了测量仪器满足海森伯关系的严格条件。特别地，证明了噪声和干扰与被测物体统计上无关的每一种仪器都满足海森伯格关系。为此，所有可能的量子测量都用自然可接受的公理来描述。在此基础上，引入了概率算子值测度与观测值之间距离的数学概念，并讨论了它的基本性质。基于这一概念，测量噪声和扰动可以在模型无关的公式中自然地定义为任何量子测量。在该公式下，还导出了具有独立噪声、独立干扰、无偏噪声和无偏干扰的装置以及无噪声装置和无干扰装置的各种噪声和干扰关系。根据新的不确定度关系讨论了位置测量的两种模型，表明即使是近似可重复的位置测量也可以违反海森堡关系。(C)2004 Elsevier Inc.保留所有权利。
Heisenberg's uncertainty relation for measurement noise and disturbance is commonly understood to state that in any measurement the product of the position measurement noise and the momentum disturbance is not less than Planck's constant divided by 4pi. However, it has been shown in many ways that this relation holds only for a restricted class of measuring apparatuses in the most general formulation of measuring processes. Here, Heisenberg's uncertainty relation is generalized to a relation that holds for all the possible quantum measurements, from which rigorous conditions are obtained for measuring apparatuses to satisfy Heisenberg's relation. In particular, every apparatus with the noise and the disturbance statistically independent from the measured object is proven to satisfy Heisenberg's relation. For this purpose, all the possible quantum measurements are characterized by naturally acceptable axioms. Then, a mathematical notion of the distance between probability operator valued measures and observables is introduced and the basic properties are explored. Based on this notion, the measurement noise and disturbance are naturally defined for any quantum measurements in a model independent formulation. Under this formulation, various relations for noise and disturbance are also derived for apparatuses with independent noise, independent disturbance, unbiased noise, and unbiased disturbance as well as noiseless apparatuses and nondisturbing apparatuses. Two models of position measurements are also discussed in the light of the new uncertainty relations to show that Heisenberg's relation can be violated even by approximately repeatable position measurements. (C) 2004 Elsevier Inc. All rights reserved.