Schrödinger (Nature, v.169, 538 (1952)) noted that the complex matter field in the Klein-Gordon equation can be made real by a gauge transform, although charged fields are believed to require complex functions. Surprisingly, the result can be extended to the Dirac equation: three complex components of the Dirac spinor function can be algebraically eliminated, and the remaining component can be made real by a gauge transform. Therefore, the Dirac equation is generally equivalent to one fourth-order partial differential equation for one real function (A. Akhmeteli, J. Math. Phys. v.52, 082303 (2011)). These results both belong in textbooks and can be used for development of new efficient methods of quantum chemistry. The matter field can be algebraically eliminated both in scalar electrodynamics and in spinor electrodynamics in a certain gauge. The resulting equations describe independent dynamics of the electromagnetic field, which permits mathematical simplification and can be useful for interpretation of quantum theory. For example, in the Bohm interpretation, the electromagnetic field can replace the wave function as the guiding field. It is also shown that for these equations, generalized Carleman embedding generates systems of linear equations in the Hilbert space, which look like second-quantized theories and are equivalent to the original nonlinear systems on the set of solutions of the latter. Thus, the relevant local realistic models can be embedded into quantum field theories. These models are equivalent to scalar electrodynamics and spinor electrodynamics, so they correctly describe a large body of experimental data. Although they may need some modifications for better agreement with experiments, they may be of great interest as "no drama quantum theories", as simple (in principle) as classical electrodynamics. Possible issues with the Bell theorem are discussed.
This article builds on recent work (A. Akhmeteli, Int'l Journ. of Quantum Information, vol. 9, Suppl. (2011) p. 17, and A. Akhmeteli, Journ. Math. Phys., vol. 52 (2011) p. 082303), providing a theory that is based on spinor electrodynamics, is described by a system of partial differential equations in 3+1 dimensions, but reproduces unitary evolution of a quantum field theory in the Fock space. To this end, after introduction of a complex four-potential of electromagnetic field, which generates the same electromagnetic fields as the initial real four-potential, spinor field is algebraically eli…
This work builds on the following result of a previous article (quant-ph/0509044): the matter field can be naturally eliminated from the equations of the scalar electrodynamics (the Klein-Gordon-Maxwell electrodynamics) in the unitary gauge. The resulting equations describe independent dynamics of the electromagnetic field (they form a closed system of partial differential equations). An improved derivation of this surprising result is offered in the current work. It is also shown that for this system of equations, a generalized Carleman linearization (Carleman embedding) procedure generates a…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematic…
Topos theory has been suggested by Döring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of physics is and what its conceptual framework looks like. The motivation of using topos theory to express quantum theory lies in the desire to overcome certain interpretational problems inherent in the standard formulation of the theory. In particular, the topos reformulation of quantum theory overcomes the instrumentalist/Copenhagen interpretation thereby rendering …
In the first half we make a short review of coherent states and generalized coherent ones based on Lie algebras su(2) and su(1,1), and the Schwinger's boson method to construct representations of the Lie algebras. In the second half we make a review of recent developments on both swap of coherent states and cloning of coherent states which are important subjects in Quantum Information Theory.
This is a comment on the paper : Quantum Interference between Light Sources Separated by 150 Million Kilometers by Deng et al, PHYSICAL REVIEW LETTERS 123, 080401 (2019)
Omnes' interpretation of quantum mechanics is summarized, and compared with other consistent-history approaches by Gell-Mann and Hartle, and by Griffiths.
The mechanism of spontaneous symmetry breaking in quantum systems is briefly reviewed, rectifying part of the standard wisdom on logical and mathematical grounds. The crucial role of the localization properties of the time evolution for the conclusion of the Goldstone theorem is emphasized.
In Stephen Adler's book, "Quantum theory as an emergent phenomenon," the author starts from a classical mechanics structure and "derives" the formalism of quantum theory, together with wave function collapse dynamics, the latter providing the interpretation of quantum theory. A detailed outline of the author's argument is presented in this book review.
This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary…
Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology, decision making, information processing, especially information retrieval. The latter is very promising. The aim of this brief introductory review is to stimulate research in this exciting area of information science. This paper is not aimed to present a complete review on the state of art in quantum information retrieval.
In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject, we consider if quantum non-locality, and the friction it carries with special relativity, can eventually find a "solution" by considering higher dimensional spaces.
This article reviews the 2008 quantum algorithm for linear systems of equations due to Harrow, Hassidim and Lloyd, as well as some of the followup and related work. It was submitted to the Springer Encyclopedia of Algorithms.
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory and several detailed applications to practical situtations.
In ``Quantum Evolution: Life in the Multiverse'' (HarperCollins, 2000), ISBN 0-00-255948-X, 0-00-655128-9, Johnjoe McFadden makes far-reaching claims for the importance of quantum physics in the solution of problems in biological science. In this review, I discuss the relevance of unitary wavefunction dynamics to biological systems, analyse the inverse quantum Zeno effect, and argue that McFadden's use of quantum theory is deeply flawed.
This paper is a response to the critical review by Mathew J. Donald of the popular science book 'Quantum Evolution' by Johnjoe McFadden and our earlier paper (by Johnjoe McFadden and Jim Al-Khalili), in which we propose a quantum mechanical explanation for certain types of mutation. We here address Donald's criticisms and reassert our proposal.
We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.
We review recent research on quantum glasses, with a focus on their equilibrium dynamics and the interplay between glassiness and localization phenomena. Interesting relations with the SYK model are discussed.
Self-testing is a method to infer the underlying physics of a quantum experiment in a black box scenario. As such it represents the strongest form of certification for quantum systems. In recent years a considerable self-testing literature has been developed, leading to progress in related device-independent quantum information protocols and deepening our understanding of quantum correlations. In this work we give a thorough and self-contained introduction and review of self-testing and its application to other areas of quantum information.
We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.
Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks which not only give rise to physically meaningful correlations of holographic boundary states, but also reproduce and refine features of quantum error correction in holography. This topical review provides an overview over recent successful realizations of such models. It does so by building on an …
We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.
Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the quantum annealing algorithm for programmable use. Specifically, quantum annealing processors produced by D-Wave Systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for quantum ann…
We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how this controversy has affected the development of the subject.
In this proceeding I review the main experimental results obtained at IENGF (Turin, Italy) by using a source of entangled photons realised superposing, by means of an optical condenser, type I PDC produced in two crystals. More in details, after having described how this source is built, I will report on a Bell inequalities test obtained with it. Then I describe a recent innovative double slit experiment realised with a similar scheme. Finally, I hint about future developments of this activity at IENGF and in particular about a quantum cryptographic scheme in d=4.
Over the last two decades, tremendous advances have been made for constructing large-scale quantum computers. In particular, the quantum processor architecture based on superconducting qubits has become the leading candidate for scalable quantum computing platform, and the milestone of demonstrating quantum supremacy was first achieved using 53 superconducting qubits in 2019. In this work, we provide a brief review on the experimental efforts towards building a large-scale superconducting quantum computer, including qubit design, quantum control, readout techniques, and the implementations of …
Blockchain technology is facing critical issues of scalability, efficiency and sustainability. These problems are necessary to solve if blockchain is to become a technology that can be used responsibly. Useful quantum computers could potentially be developed by the time that blockchain will be widely implemented for mission-critical work at financial and other institutions. Quantum computing will not only cause challenges for blockchain, but can also be harnessed to better implement parts of blockchain technologies including cryptocurrencies. We review the work that has been done in the area o…
Lasers and LEDs display a statistical distribution in the number of photons emitted in a given time interval. New applications exploiting the quantum properties of light require sources for which either individual photons, or pairs, are generated in a regulated stream. Here we review recent research on single-photon sources based on the emission of a single semiconductor quantum dot. In just a few years remarkable progress has been made in generating indistinguishable single-photons and entangled photon pairs using such structures. It suggests it may be possible to realise compact, robust, LED…
Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, we review the existing quantum CKA protocols based on multipartite entanglement, both in the device-dependent and the device-independent scenario.
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approa…
In this paper, we note that there are two different types of inconsistencies of quantum adiabatic theorem in work of K. P. Marzlin and B. C. Sanders [Phys. Rev. Lett. 93, 160408, 2004], MS inconsistency and MS counterexample. Nevertheless, these two types are often confused as one by many authors. We shall point out that the inconsistencies of quantum adiabatic theorem raised by the relevant references just can be classified as these two types.
This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an…
There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to the non-intuitive nature of quantum algorithms to the classically trained person. Thus, the idea of using computers to automatically generate quantum algorithms based on an evolutionary model emerged. A limitation of this approach is that quantum computers do not yet exist and quantum simulation on a classical machine has an exponential order overhead. Neverth…
Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Its aim is to develop primitives beyond the reach of classical cryptography or to improve on existing classical implementations. Although much of the work in this field is dedicated to quantum key distribution (QKD), some important steps were made towards the study and development of quantum oblivious transfer (QOT). It is possible to draw a comparison between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quant…
Diamond quantum technologies based on color centers have rapidly emerged in the most recent years. The nitrogen-vacancy (NV) color center has attracted a particular interest, thanks to its outstanding spin properties and optical addressability. The NV center has been used to realize innovative multimode quantum-enhanced sensors that offer an unprecedented combination of high sensitivity and spatial resolution at room temperature. The technological progress and the widening of potential sensing applications have induced an increasing demand for performance advances of NV quantum sensors. Quantu…
The desire to obtain an unconditionally secure bit commitment protocol in quantum cryptography was expressed for the first time thirteen years ago. Bit commitment is sufficient in quantum cryptography to realize a variety of applications with unconditional security. In 1993, a quantum bit commitment protocol was proposed together with a security proof. However, a basic flaw in the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau. Later the result was generalized by Mayers who showed that unconditionally secure bit commitment is impossible. A brief review on quantum bit…
This is an extended essay review of Tanya and Jeffrey Bub's Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. Princeton and Oxford: Princeton University Press (2018), ISBN: 9780691176956, 272 pp., 7x10 in., 254 b/w illus., £18.99 / $22.95 (paperback). We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors' artistic choices in the context of comics theory.
The recent advances in single atom detection and manipulation in experiments with ultracold quantum gases are reviewed. The discussion starts with the basic principles of trapping, cooling and detecting single ions and atoms. The realization of single atom detection in ultracold quantum gases is presented in detail and the employed methods, which are based on light scattering, electron scattering, field ionization and direct neutral particle detection are discussed. The microscopic coherent manipulation of single atoms in a quantum gas is also covered. Various examples are given in order to hi…
The so-called contemporary AI revolution has reached every corner of the social, human and natural sciences -- physics included. In the context of quantum many-body physics, its intersection with machine learning has configured a high-impact interdisciplinary field of study; with the arise of recent seminal contributions that have derived in a large number of publications. One particular research line of such field of study is the so-called Neural-Network Quantum States, a powerful variational computational methodology for the solution of quantum many-body systems that has proven to compete wi…
Quantum information processing based on Rydberg atoms emerged as a promising direction two decades ago. Recent experimental and theoretical progresses have shined exciting light on this avenue. In this concise review, we will briefly introduce the basics of Rydberg atoms and their recent applications in associated areas of neutral atom quantum computation and simulation. We shall also include related discussions on quantum optics with Rydberg atomic ensembles, which are increasingly used to explore quantum computation and quantum simulation with photons.
The development of techniques for manipulation of quantum information has opened the door to a variety of protocols for accomplishing unprecedented tasks. In particular, a new protocol of quantum teleportation was proposed in 2008 to achieve effective energy transportation simply via local operations and classical communication without breaking any known physical laws. This is achieved by extracting zero-point energy of entangled many-body systems by local operations dependent on information obtained by a distant measurement. The concept is reviewed from an introductory viewpoint herein.
Quantum Teleportation toward the Quantum Internet: A Concise Review
University of Electronic Science and Technology of China（电子科技大学）；Southwest Institute of Technical Physics（西南技术物理研究所）；AMS（中国科学院数学与系统科学研究院）；Tianfu Jiangxi Laboratory（天府江西实验室）；University of Science and Technology of China（中国科学技术大学）
Book chapter in "Thermodynamics in the quantum regime - Recent Progress and Outlook" -- This chapter is a survey of the published literature on quantum batteries -- ensembles of non-degenerate quantum systems on which energy can be deposited, and from which work can be extracted. A pedagogical approach is used to familiarize the reader with the main results obtained in this field, starting from simple examples and proceeding with in-depth analysis. An outlook for the field and future developments are discussed at the end of the chapter.
The processing of information and computation is undergoing a paradigmatic shift since the realization of the enormous potential of quantum features to perform these tasks. Coupled cavity array is one of the well-studied systems to carry out these tasks. It is a versatile platform for quantum networks for distributed information processing and communication. Cavities have the salient feature of retaining photons for longer durations, thereby enabling them to travel coherently through the array without losing them in dissipation. Many quantum information protocols have been implemented in array…
For a large number of tasks, quantum computing demonstrates the potential for exponential acceleration over classical computing. In the NISQ era, variable-component subcircuits enable applications of quantum computing. To reduce the inherent noise and qubit size limitations of quantum computers, existing research has improved the accuracy and efficiency of Variational Quantum Algorithm (VQA). In this paper, we explore the various ansatz improvement methods for VQAs at the gate level and pulse level, and classify, evaluate and summarize them.
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements.
We perform a review of various approaches to the implementation of quantum memories, with an emphasis on activities within the quantum memory sub-project of the EU Integrated Project "Qubit Applications". We begin with a brief overview over different applications for quantum memories and different types of quantum memories. We discuss the most important criteria for assessing quantum memory performance and the most important physical requirements. Then we review the different approaches represented in "Qubit Applications" in some detail. They include solid-state atomic ensembles, NV centers, q…
We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expres…
