Quantum-mechanical Background Research Articles

On the statistical background of quantum mechanics: generalities and a concrete example

We revisit our description of randomness in quantum processes that began in collaboration of Jean Ginibre. The calculations were performed on a worked example: the fluorescence of a single two-level atom pumped by a resonant laser field. This pump laser is described classically (by a function, not an operator). Our aim is first to built a Kolmogorov-type equation (K-equation) for the atomic state, so that the two parameters θ, φ that define this density matrix are random functions of time, therefore the atomic density matrix is a random density matrix. Such an approach, initiated for gas kinetics, was not yet applied to quantum phenomena, whereas it is especially tailored to very quick events well separated (in time) like the quantum jumps observed in spontaneous emission of photons by an atom. Here, we try to clarify the basis of our statistical approach leading to the K-equation below, and we present the main results deduced from it. We explain finally that our approach can be interpreted in terms of Everett’s theory of many-worlds, because at every emission a new history begins for the atom, with two nonoverlapping wave functions.

Quantum error-correcting codes and their geometries

This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum error-correcting codes allow the negation of these effects in order to successfully restore the original quantum information. We briefly describe the necessary quantum-mechanical background to be able to understand how quantum error correction works. We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension. We will delve into the geometry of these codes. This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters. We also include sections on quantum maximum distance separable codes and the quantum MacWilliams identities.

Quantum Communication Networks

This book on quantum mechanics is structured into seven chapters with a comprehensive list of over 200 recent references. Quantum mechanics was born over 100 years ago and has attracted fundamental research first in mathematics and physics, then in computing and information theory, and finally in wireless communications. The following topics are covered: the history of the evolution of classical communication networks; the background of quantum mechanics; an understanding of these key quantum ideas that are important in quantum computation; quantum equivalents of basic Shannon information-theoretic tasks; forward error correction codes; future quantum communication architecture; and some interesting use cases for quantum communication networks. Clock synchronization, exchanging Cartesian reference frames, and interferometry. The book prepares the reader to take the next step toward quantum network systems design. The reader is convinced that quantum-mechanical resources will become an important part in the effective and efficient evolution of future wireless communication networks. The book provides all researchers who will enter this exciting field with a valuable reference for the

Very brief on quantum computing with special respect to ion traps technology

Because of the continuing miniaturization of integrated circuits it appears that quantum phenomena will play a more and more dominant role in their design and functioning. Therefore, the work exposes concise quantum mechanical and mathematical background of quantum phenomena based computing through the introduction of concepts such as Hilbert space, qubit, Bloch sphere, quantum gate and measurement. Recent improvements in ion- trap technology based computing suggest ion- trap technology as the most promising one for use in quantum computing. So, the paper describes the ion- trap based technology, its use in quantum computation and its latest applications in quantum computing. It turns out that recent ion- trap technology based computers dramatically improves on all of the Vincenzo’s criterions.

Quantum thermodynamics aspects with a thermal reservoir based on -symmetric Hamiltonians

We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on -symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the -symmetric features of the reservoir allows to reverse the heat flow between system and reservoir, as well as to preserve the coherence over a longer period of time and reduce the entropy production. Furthermore, we considered a modified quantum Otto cycle in which the standard hot thermal reservoir is replaced by the thermal reservoir based on -symmetric Hamiltonians. By defining an effective temperature depending on the -symmetric parameter, it is possible to interchange the quantum Otto cycle configuration from engine to refrigerator by varying the -symmetric parameter. Our results indicate that -symmetric effects could be useful to achieve an improvement in quantum thermodynamics protocols such as coherence protection and entropy production reduction.

Experimental methods in chemical engineering: Density functional theory

AbstractDensity functional theory (DFT) computations apply to physics, chemistry, material science, and engineering. In chemical engineering, DFT identifies material structure and properties, and mechanisms for phenomena such as chemical reaction and phase transformation that are otherwise impossible to measure experimentally. Even though its practical application dates back only a decade or two, it is already a standard tool for materials modelling. Many textbooks and articles describe the theoretical basis of DFT, but it remains difficult for researchers to autonomously learn the steps to accurately calculate system properties. Here, we first explain the foundations of DFT in a way accessible to chemical engineers with little background in quantum mechanics or solid‐state physics. Then, we introduce the basics of the computations and, for most of the rest of the article, we show how to derive physical characteristics of interest to chemical engineers: elastic, thermodynamic, and surface properties, electronic structure, and surface and chemical reaction energy. Finally, we highlight some limitations of DFT; since these calculations are approximations to the Schrödinger equation, their accuracy relies on choosing adequate exchange‐correlation functions and basis sets. Since 1991, the number of articles WoS has indexed related to DFT has increased quadratically with respect to time and now numbers 15 000. A bibliometric analysis of the top 10 000 cited articles in 2018 and 2019 classifies them into four clusters: adsorption, graphene, and nanoparticles; ab initio molecular dynamics and crystal structure; electronic structure and optical properties; and total energy calculations and wave basis sets.

The principle of similars and importance of arsenic compound as a preventive against Covid-19

In homeopathy, special importance is attributed to the Law of Similars (SimiliaSimilibusCurentur, or “let likes be cured by likes.”). But an in- depth analysis of this principle is still necessary and important for exploring the science behind diluted homeopathic medicine (or Homed).Recently it has been suggested that Arsenicum album 30 (prepared from arsenic compound) might be a curable preventive medicine against Coronavirus infections. But the recommendation for the use of Arsenicum album 30 or similar other medicines as a preventive against Covid-19 are not beyond doubt as this preventive has not been scientifically supported. This is mainly due to the unknown mechanism of the said principle of Similars. The symptoms in this principle are viewed as direct manifestation of the diseases to be cured. There exists close relation between the mechanisms of curing diseases by the Homed and the body’s self healing (or homeostasis related to T-Cells) which is stimulated by Homed to cure the disease. We find incipient quantum mechanical background of this principle and attempted to justify the use of Arsenicum or similar other medicine against Corona infection based on this principle. The principle of Similars has quantum biological foundation arising from quantum coherence (QC)between the ionic charges around the diseased cell and the carrier of diseased cell and those associated with the medicinal agent present in the Homed termed as NAM (H- bonded nano and micros clusters).This principle justifies the use of Arsenicum against the Corona infection. It is demonstrated that the principle of Similars has a deeper incipient meaning rooted to the quantum mechanics. This principle is competent to explain many salient features of homeopathy.

Quantum Computer Systems: Research for Noisy Intermediate-Scale Quantum Computers

This book targets computer scientists and engineers who are familiar with concepts in classical computer systems but are curious to learn the general architecture of quantum computing systems. It gives a concise presentation of this new paradigm of computing from a computer systems' point of view without assuming any background in quantum mechanics. As such, it is divided into two parts. The first part of the book provides a gentle overview on the fundamental principles of the quantum theory and their implications for computing. The second part is devoted to state-of-the-art research in designing practical quantum programs, building a scalable software systems stack, and controlling quantum hardware components. Most chapters end with a summary and an outlook for future directions. This book celebrates the remarkable progress that scientists across disciplines have made in the past decades and reveals what roles computer scientists and engineers can play to enable practical-scale quantum computing.

Quantum-mechanical simulations for in vivo MR spectroscopy: Principles and possibilities demonstrated with the program NMRScopeB

Current possibilities and limitations of the simulation of in vivo magnetic resonance spectroscopic signals are demonstrated from the point of view of a simulation software user as well as its programmer. A brief review of the quantum-mechanical background addresses the specific needs of simulation implementation and in vivo MR spectroscopy in general. Practical application examples demonstrate how flexible simulation software, such as NMRScopeB, can be utilized not only for the preparation of metabolite basis signals for quantification of metabolite concentrations, but also in pulse sequence development, assessment of artifacts and analyzing mechanism leading to unexpected signal phenomena.

Effects of the generalised uncertainty principle on quantum tunnelling

In a previous paper (Blado et al 2014 Eur. J. Phys. 35 065011), we showed that quantum gravity effects can be discussed with only a background in non-relativistic quantum mechanics at the undergraduate level by looking at the effect of the generalised uncertainty principle (GUP) on the finite and infinite square wells. In this paper, we derive the GUP corrections to the tunnelling probability of simple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models of quantum cosmogenesis and gravitational tunnelling radiation) and which employ the WKB approximation, a topic discussed in undergraduate quantum mechanics classes. It is shown that the GUP correction increases the tunnelling probability in each of the examples discussed.

Lectures on Geometric Quantization

These lectures notes are meant as an introduction to geometric quantization. In Section 1, I begin with presentation of the historical background of quantum mechanics. I continue with discoveries in the theory of representations of Lie groups, which lead to emergence of geometric quantization as a part of pure mathematics. This presentation is very subjective, flavored by my own understanding of the role of geometric quantization in quantum mechanics and representation theory. Section 2 is devoted to a review of geometry of Hamiltonian systems. Geometric quantization is discussed in the next two sections: prequantization in Section 3 and polarization in Section 4. In particular, I discuss geometric quantization with respect to polarizations given by Kahler structure, cotangent bundle projection and completely integrable system. More advanced topics, like metaplectic structure, pairing of polarizations, and commutation of quantization and reduction, are not included.

The Heteronuclear Single-Quantum Correlation (HSQC) Experiment: Vectors versus Product Operators

A vectorial representation of the full sequence of events occurring during the 2D-NMR heteronuclear single-quantum correlation (HSQC) experiment is presented. The proposed vectorial representation conveys an understanding of the magnetization evolution during the HSQC pulse sequence for those who have little or no quantum mechanical background. This vectorial depiction is compared to results from the product operator formalism, and thus uncovers several parallelisms and subtle differences between both models. This approach permits a nice introduction to product operators at a level comprehensible to advanced upper-division undergraduate and graduate students without the use of the spin-density matrix.

Solving large-scale optimization problems related to Bell’s Theorem

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with an innovative matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve substantially larger problems. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.

Crossing disciplines ‐ A view on two‐dimensional optical spectroscopy

Recent interest in the role of quantum mechanics in the primary events of photosynthetic energy transfer has led to a convergence of nonlinear optical spectroscopy, condensed matter and quantum physics on the topic of energy‐transfer dynamics in pigment‐protein complexes. The convergence of these communities has unveiled a mismatch between the background and terminology of the respective fields. To make connections, a pedagogical guide to understanding the basics of two‐dimensional spectra is provided aimed at researchers with a background in quantum mechanics and condensed matter.

Quantum computing and communications – Introduction and challenges

Computer engineers are continuously seeking new solutions to increase available processing speed, achievable transmission rates, and efficiency in order to satisfy users’ expectations. While multi-core systems, computing clouds, and other parallel processing techniques dominate current technology trends, elementary particles governed by quantum mechanics have been borrowed from the physicists’ laboratory and applied to computer engineering in the efforts to solve sophisticated computing and communications problems. In this paper, we review the quantum mechanical background of quantum computing from an engineering point of view and describe the possibilities offered by quantum-assisted and quantum-based computing and communications. In addition to the currently available solutions, the corresponding challenges will also be surveyed.

Tutorial on analytic theory for cross‐polarization in solid state NMR

AbstractThis tutorial aims to be a self‐contained and explicit analysis of the basic cross polarization (CP) solid‐state NMR experiment (SSNMR) in the isolated spin‐pair approximation using standard quantum mechanical arguments. The general result of obtaining coherence transfer between two dipolar coupled spin‐active nuclei while applying radio frequency fields to both nuclei is described, with emphasis on the origin of the well known Hartmann‐Hahn matching conditions. No new theory is presented; rather several common analytical methods in SSNMR are demonstrated in the context of cross‐polarization under static and magic‐angle spinning (MAS) conditions. A background in NMR and quantum mechanics is assumed, however this work attempts to minimize the need for excursions into the literature. This article was written to aid a reader in advancing into more detailed descriptions of CP and dipolar recoupling in general. © 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part A 32A: 254–276, 2008.

Emergence of classical reality from a quantum mechanical background

A model for the process of knowledge acquisition is presented that shows how naive realism emerges from a quantum mechanical background. We formalise this process of emergence and obtain in this way an illustrative insight to some of the most fundamental physical theories: GRW-theory and E ∞-theory.

Quantum cryptography

We survey some results in quantum cryptography. After a brief introduction to classical cryptography, we provide the quantum-mechanical background needed to present some fundamental protocols from quantum cryptography. In particular, we review quantum key distribution via the BB84 protocol and its security proof, as well as the related quantum bit commitment protocol and its proof of insecurity.

Donald Edward Osterbrock

Donald Edward Osterbrock

A short introduction to quantum information and quantum computation

Quantum information and computation is a rapidly expanding and cross-disciplinary subject. This book, first published in 2006, gives a self-contained introduction to the field for physicists, mathematicians and computer scientists who want to know more about this exciting subject. After a step-by-step introduction to the quantum bit (qubit) and its main properties, the author presents the necessary background in quantum mechanics. The core of the subject, quantum computation, is illustrated by a detailed treatment of three quantum algorithms: Deutsch, Grover and Shor. The final chapters are devoted to the physical implementation of quantum computers, including the most recent aspects, such as superconducting qubits and quantum dots, and to a short account of quantum information. Written at a level suitable for undergraduates in physical sciences, no previous knowledge of quantum mechanics is assumed, and only elementary notions of physics are required. The book includes many short exercises, with solutions available to instructors through solutions@cambridge.org.