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。
英文摘要：
Previously, Bennet and Feynman asked if Heisenberg's uncertainty principle puts a limitation on a quantum computer (Quantum Mechanical Computers, Richard P. Feynman, Foundations of Physics, Vol. 16, No. 6, p597-531, 1986). Feynman's answer was negative. In this paper, we will revisit the same question for the discrete time Fourier transform uncertainty principle. We will show that the discrete time Fourier transform uncertainty principle plays a fundamental role in showing that Shor's type of quantum algorithms has efficient running time and conclude that the discrete time uncertainty principle is an aid in our current formulation and understanding of Shor's type of quantum algorithms. It turns out that for these algorithms, the probability of measuring an element in some set $T$ (at the end of the algorithm) can be written in terms of the time-limiting and band-limiting operators from finite Fourier analysis. Associated with these operators is the finite Fourier transform uncertainty principle. The uncertainty principle provides a lower bound for the above probability. We will derive lower bounds for these types of probabilities in general. We will call these lower bounds quantum algorithm uncertainty principles or QAUP. QAUP are important because they give us some sense of the probability of measuring something desirable. We will use these lower bounds to derive Shor's factoring and discrete log algorithms.
The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner Distribution; Relation With the Notion of Symplectic Capacity
