Uncertainty relation and probability: Numerical illustration
Uncertainty relation and probability: Numerical illustration
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不确定性关系和概率：数值说明
DOI：
10.1143/ptp.125.205
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
K. Fujikawa and K. Umetsu
中科院分区：
文献类型：
--
作者：
M. Chaichian;K. Fujikawa and A. Tureanu;谷村省吾;K. Fujikawa;谷村省吾;谷村省吾;Kazuo Fujikawa;谷村省吾;K. Fujikawa;谷村省吾;谷村省吾;K. Fujikawa and K. Umetsu
量子力学的测不准关系和概率解释有着内在的联系，标准差的计算就是明证。因此，很自然地会问，人们是否可以将适当抽样事件的非常小的不确定度乘积与非常小的概率联系起来。我们在其他地方已经表明，过去提到的回避不确定关系的一些例子实际上是这样理解的。我们在这里数值说明，如果对以非常小的概率出现的测量数据进行适当的采样，则实现了非常小的不确定度积。我们引入了循环测量的概念。结果还表明，我们的分析与Landau-Pollak型测不准关系是一致的。本文的分析可能有助于调和关于引力波探测中“标准量子极限”的相互矛盾的观点。
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data that occur with a very small probability. We introduce a notion of cyclic measurements. It is also shown that our analysis is consistent with the Landau-Pollak-type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the “standard quantum limit” in the detection of gravitational waves.