A discrete-event simulation approach which provides a cause-and-effect description of many experiments with photons and neutrons exhibiting interference and entanglement is applied to a recent single-neutron experiment that tests (generalizations of) Heisenberg's uncertainty relation. The event-based simulation algorithm reproduces the results of the quantum theoretical description of the experiment but does not require the knowledge of the solution of a wave equation nor does it rely on concepts of quantum theory. In particular, the data satisfies uncertainty relations derived in the context of quantum theory.
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their properties. Further, we apply a similar technique to measure the uncertainty in the preparation of a quantum state.
Tight qubit uncertainty relations studied through weak values in neutron interferometry
Atominstitut, TU Wien（维也纳工业大学原子研究所）；Department of Applied Physics, Hokkaido University（北海道大学应用物理系）；Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；Institut Laue Langevin（劳厄-朗之万研究所）
One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain, with the help of periodic coarse graining. Here we consider the whole family of Rényi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.
在此之前，Bennet和Feynman问海森堡的不确定原理是否对量子计算机有限制（Quantum Mechanical Computers，Richard P. Feynman，Foundations of Physics，Vol. 16，No. 6，p597-531，1986）。费曼的回答是否定的。在本文中，我们将重新讨论离散时间傅里叶变换的不确定原理的相同问题。我们将表明，离散时间傅立叶变换不确定原理起着根本性的作用，表明肖尔的量子算法的类型具有有效的运行时间，并得出结论，离散时间不确定原理是一个援助，在我们目前的制定和理解肖尔的量子算法的类型。事实证明，对于这些算法，测量某个集合$T$中的元素的概率（在算法结束时）可以用有限傅立叶分析的时间限制和频带限制算子来表示。与这些算子相联系的是有限傅里叶变换不确定原理。不确定原理为上述概率提供了一个下限。我们将推导出这些类型的概率的一般下界。我们将这些下界称为量子算法不确定原理或QAUP。QAUP之所以重要，是因为它们让我们对衡量某些可取之处的概率有了一些了解。我们将使用这些下界来推导Shor的因子分解和离散对数算法。
