Uncertainty principle for joint measurement of noncommuting variables
Uncertainty principle for joint measurement of noncommuting variables
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非交换变量联合测量的不确定性原理
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
M. Raymer
中科院分区：
文献类型：
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作者：
M. Raymer
海森堡测不准原理是指测量误差，还是指粒子状态固有的物理变量值的扩散，还是指这些的某种组合？不确定性原理最常被引用的形式是将某个变量的单独测量的集合的扩展与其共轭变量的类似扩展联系起来。相反，海森堡最初的不确定性原理的论证涉及到一个变量的测量对粒子状态的扰动，这影响了人们预测共轭变量的后续测量结果的能力。本文讨论了测不准原理的这两种观点之间的关系。一个熟悉的例子被认为是：一个合奏的同样准备粒子通过狭缝，并在进一步传播被检测。从这种安排，它是可能的联合推断（虽然不一定精确）的横向位置和共轭动量为合奏的每个成员的信息。结果表明，在这种情况下，联合测量的产品的测量结果的标准偏差是至少两倍大的下限所隐含的通常的不确定性原则。讨论的目的是帮助澄清初始状态和测量误差在不确定性原理的各种陈述中所起的不同作用。
Does the Heisenberg uncertainty principle refer to errors of measurement, or to the spread of values of the physical variables intrinsic to a particle’s state, or to some combination of these? The most commonly quoted form of the uncertainty principle relates the spread of an ensemble of separate measurements of some variable to the analogous spread of its conjugate variable. In contrast, Heisenberg’s original argument for the uncertainty principle involved the perturbation to a particle’s state by a measurement of one variable, which affects one’s ability to predict the outcome of a subsequent measurement of the conjugate variable. The relation between these two views of the uncertainty principle is discussed in this paper. A familiar example is considered: an ensemble of identically prepared particles passing through a slit, and after further propagation being detected. From this arrangement it is possible to infer joint (although necessarily imprecise) information on both transverse position and conjugate momentum for each member of the ensemble. It is shown that in this case of joint measurement the product of standard deviations for the measurement outcomes is at least twice as large as the lower bound implied by the usual uncertainty principle. The discussion is meant to help clarify the different roles played in the various statements of the uncertainty principle by the initial state and by measurement error.