A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised definition. The metric of quantum states in the configuration space and its possible geometrical framework is explored. Also, invariance of the metric of quantum states under local gauge transformations, coordinate transformations, and the relativistic transformations is discussed.
We revisit the quantum phase operator $Φ$ introduced by Garrison and Wong. Denoting by $N$ the number operator, we provide a detailed proof of the Heisenberg commutation relation $ΦN - NΦ= iI$ on the natural maximal domain $D(ΦN) \cap D(N Φ)$ as well as the failure of the Weyl commutation relations, and discuss some further interesting properties of this pair.
We stand by our findings in Phys. Rev A. 96, 022126 (2017). In addition to refuting the invalid objections raised by Peleg and Vaidman, we report a retrocausation problem inherent in Vaidman's definition of the past of a quantum particle.
Three variants of the Garrett approximation are studied and their accuracy is analyzed, for symmetric and asymmetric square wells. Quite surprisingly, the simplest variants are also the most accurate. The applications to quantum wells, quantum dots and capillary neutron guides are briefly discussed.
Quantum Data Compression and Relative Entropy Revisited
B. Schumacher和M. Westmoreland建立了一个量子模拟的一个著名的经典信息理论结果的作用，相对熵作为一个衡量非最优的（经典）数据压缩。在本文中，我们提供了一个替代的，简单的和建设性的证明这一结果，通过构造量子压缩码（计划）从经典的数据压缩码。此外，由于量子数据压缩/编码任务可以有效地减少到一个（准）经典的，我们表明，从经典信息理论和数据压缩的相关结果变得适用，因此可以扩展到量子域。
将Kirkpatrick的经典三箱悖论[J. Phys. A 36 4891（2003）]与Aharonov和Vaidman的原始量子三箱悖论[J. Phys. A 24 2315（1991）]进行了比较。有人认为，量子三盒实验是一个“量子悖论”，在这个意义上，它是一个经典的任务，不能使用经典的手段来完成，但可以使用量子设备来完成的一个例子。它表明，柯克帕特里克的纸牌游戏是类似于一个不同的游戏与粒子在三个盒子，其中不包含矛盾的功能。
作为旧量子理论的续篇，在对新量子力学的“教科书“解释进行了全景式的介绍之后，在爱因斯坦和尼尔斯·玻尔以来的各种建议的背景下，对自哥本哈根解释以来的量子理论的概念基础进行了回顾，旨在阐明与其基础有关的可能的新方面，其固有的“不完整性”的关键问题是A）测量，和B）量子非定域性。本文还简要介绍了与量子芝诺效应有关的测量问题，即量子芝诺效应和反芝诺效应。新方面的投入来自一些重要的印度专家：S.M. Roy，V. Singh ; D. B. Misra; C.S.乌尼克里希南
The recent criticism of Vaidman's propsal for the analysis of the past of a particle in the nested interferometer is refuted. It is shown that the definition of the past of the particle adopted by Englert et al. [Phys. Rev. A 96, 022126 (2017)] is applicable only to a tiny fraction of photons in the interferometer which indeed exhibit different behaviour. Their proof that all pre- and postselected particles behave this way, i.e. follow a continuous trajectory, does not hold, because it relies on the assumption that it is intended to prove.
The Bell inequalities stand at the cornerstone of the developments of quantum theory on both the foundational and applied side. The discussion started as a way to test whether the quantum description of reality is complete or not, but it developed in such a way that a new research area stemmed from it, namely quantum information. Far from being and exhausted topic, in the present paper we present a constructive and geometrically intuitive description of the local polytope and its facets in a bipartite Bell scenario with two dichotomic measurements per party.
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In particular, some corrections are also made in previous theoretical calculations. The corrected polynomial solutions are confronted with numerical calculations based on the Numerov method, in a good agreement between both. Then, new solutions considering the $1/r$ and $\ln r$ Coulombian-like potentials in (1+2)D, not yet obtained, are discussed numerically. In pa…
所谓的\emph{quantum game theory}是近年来量子信息理论和博弈论发展的新分支之一。然而，量子博弈本身的概念从未被严格定义，这导致了不同作者之间的许多概念混淆。在本文中，我们介绍了一个新的概念框架的\emph{scenario}和一个\emph{implementation}的游戏。它表明，在文献中提出的游戏的“量化”的程序，实际上导致几个不同的游戏，可以定义在同一个场景中，但除此之外，他们可能没有什么共同点与原来的游戏。在我们提出的框架内，围绕“量子博弈”产生的许多概念误解都可以得到明确的陈述和独特的解决。特别是，在几个静态的"量子游戏"，以及它们与贝尔不等式的连接，宣称的纠缠的重要作用，被推翻。
We formulate the Lagrangian of the Newtonian cosmology where the cosmological constant is also introduced. Following the affine quantization procedure, the Hamiltonian operator is derived. The wave functions of the Newtonian universe and the corresponding eigenvalues for the case of matter dominated by a negative cosmological constant are given.
Marcella in 2002 published a "quantum-mechanical" treatment of the famous single- and double-slit interference experiment in classical wave optics by a simple assumption that quantum mechanical wave function is a constant anywhere within a slit. Rothman and Boughn in 2011 commented that Marcella introduced no quantum physics into the problem other than\ a symbol substitution $p=\hbar k$, and the used essentially the classical wave optics. In present comment, we point out that though Marcella made a fundamental mistake, the problem is nevertheless remediable to give the satisfactory quantum mec…
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new aspect of this work is a discussion of how symmetries of a quantum system induce homomorphisms of the relevant semiheaps and ternary algebras.
In 2004 Ambainis and Regev formulated a certain form of quantum adiabatic theorem and provided an elementary proof which is especially accessible to computer scientists. Their result is achieved by discretizing the total adiabatic evolution into a sequence of unitary transformations acting on the quantum system. Here we continue this line of study by providing another elementary and shorter proof with improved bounds. Our key finding is a succinct integral representation of the difference between the target and the actual states, which yields an accurate estimation of the approximation error. …
