The Heisenberg uncertainty principle for material objects is an essential corner stone of quantum mechanics and clearly visualizes the wave nature of matter. Here we report a demonstration of the Heisenberg uncertainty principle for the most massive, complex and hottest single object so far, the fullerene molecule C70 at a temperature of 900 K. We find a good quantitative agreement with the theoretical expectation: dx * dp = h, where dx is the width of the restricting slit, dp is the momentum transfer required to deflect the fullerene to the first interference minimum and h is Planck's quantum of action.
Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of view. If a particle is prepared by a single slit of spatial width $Δx$, it has been shown that a finite standard deviation $σ_p<\infty$ can only be ensured if the wave-function is zero at the edge of $Δx$, otherwise it does not exist [8]. Under this circumstances the corresponding sharp inequality is $σ_p Δx\geq π\hbar$. This bound will be reconsidered from …
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position $x$ and momentum $p$ operators, Heisenberg's uncertainty principle points exactly to the area of the variances of $x$ and $p$. Moreover, for finite-dim…
Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we investigate the detection of entanglement via inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entangl…
Quantum devices for generating entangled states have been extensively studied and widely used. As so, it becomes necessary to verify that these devices truly work reliably and efficiently as they are specified. Here, we experimentally realize the recently proposed two-qubit entangled state verification strategies using both local measurements (nonadaptive) and active feed-forward operations (adaptive) with a photonic platform. About 3283/536 number of copies ($N$) are required to achieve a 99% confidence to verify the target quantum state for nonadaptive/adaptive strategies. These optimal stra…
In our previous work [1] we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability by exploiting the key insight classical random variables have quantum decompositions. Towards this end we built a Hilbert space of H-interpretations and a corresponding non commutative von Neu- mann algebra of bounded linear operators [2]. In this work we extend the formalism using second-quantized Horn clauses that describe processes such as Heisenberg evolu…
Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead …
本文发展了量子程序的验证方法学，其贡献有两个方面：1。Sharir，Pnueli and Hart [SIAM J. Comput. 13（1984）292 - 314]提出了一种证明概率程序性质的一般方法，该方法用马尔可夫链对概率程序进行建模，并将关于输出分布的断言扩展为关于所有中间分布的不变断言。他们的方法本质上是经典弗洛伊德归纳断言方法的概率推广。在本文中，我们考虑的量子程序模型的量子马尔可夫链的超算子定义。它表明，Sharir-Pnueli-Hart方法可以优雅地推广到量子程序，利用薛定谔-海森堡对偶量子态和可观测量。特别地，建立了量子程序的Sharir-Pnueli-Hart验证方法的完备性定理。2.正如完备性定理所指出的，Sharir-Pnueli-Hart方法原则上对于验证量子程序的所有性质都是有效的，这些性质可以用厄米算符（可观测量）来表示。但由于验证过程中涉及的计算复杂，在许多实际应用中并不可行。对于有限维状态空间的情形，我们利用超算子的矩阵表示和矩阵的Jordan分解，找到了一种比Sharir-Pnueli-Hart方法简单得多的量子程序验证方法.特别是，这种方法使我们能够很容易地计算平均运行时间，甚至可以分析量子程序在有限维状态空间中的一些有趣的长期行为。
The generation and verification of large-scale entanglement are essential to the development of quantum technologies. In this paper, we present an efficient scheme to generate genuine multipartite entanglement of a large number of qubits by using the Heisenberg interaction. This method can be conveniently implemented in various physical platforms, including superconducting, trapped-ion, and cold-atom systems. In order to characterize the entanglement of the output quantum state, we generalize the stabilizer formalism and develop an entanglement witness method. In particular, we design a generi…
Experimental Demonstration of Commutation Relations Using Intensity Correlations
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Max-Planck-Institut für die Physik des Lichts（马克斯·普朗克光科学研究所）；Universidad Complutense（康普卢顿塞大学）；Chapman University（查普曼大学）；University of Ottawa（渥太华大学）
Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
Department of Physics, Harvard University, Cambridge, MA 02138, USA（哈佛大学物理系）；Institute for Quantum Information and Matter, California Institute of Technology, CA 91125, USA（加州理工学院量子信息与物质研究所）；School of Engineering and Applied Sciences, Harvard University, Allston, Massachusetts 02134, USA（哈佛大学工程与应用科学学院）；Center for Quantum Information, IIIS, Tsinghua University, Beijing, China（清华大学信息中心）；Department of Mathematics, Duke University, Durham, NC 27708, USA（杜克大学数学系）；Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA（杜克大学电气与计算机工程系）；Duke Quantum Center, Duke University, Durham, NC 27701, USA（杜克大学量子中心）；Department of Computer Science, Virginia Tech, Alexandria, VA 22314, USA（弗吉尼亚理工大学计算机科学系）；Phasecraft Inc., Washington DC, USA（Phasecraft公司）
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a…
