Quantum Classical Correspondence And Entanglement In Periodically Driven Spin Systems
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Quantum Classical Correspondence And Entanglement In Periodically Driven Spin Systems
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Author : Meenu Kumari
language : en
Publisher:
Release Date : 2019
Quantum Classical Correspondence And Entanglement In Periodically Driven Spin Systems written by Meenu Kumari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This dissertation sets out to examine some fundamental open questions in quantum physics regarding quantum-classical correspondence in regular versus chaotic systems. Specifically, we study these questions using approaches in quantum information science in an experimentally realized textbook model of quantum chaos - the quantum kicked top (QKT). The effect of classical chaos on the generation of entanglement in spin systems has been a field of active research for a couple of decades. Whether high entanglement in these systems is a hallmark of chaos or not remains a widely debated topic. We explain the connection between entanglement and chaos in spin systems and resolve previous conflicting results. The previous studies have mostly drawn conclusions from numerical work on a few initial states in regular versus chaotic regions. We instead focus on stable and unstable periodic orbits because chaos emerges around unstable periodic orbits. We first propose a new set of criteria for determining whether quantum evolution will correspond to the classical trajectory in a localized manner at stable periodic orbits in periodically driven systems. These criteria can be used to calculate the quantum numbers that will lead to quantum-classical correspondence even in a deep quantum regime, and thus to quantify the well-known Bohr correspondence principle. Next, we analytically show a direct connection between entanglement generation and a measure of delocalization of a quantum state in spin systems. More concretely, we describe a method to calculate an upper bound on entanglement generation in any bipartition of spin systems, where the upper bound is a function of trace distance between the evolved state and the most localized classical-like separable states. This method along with our criteria for localized evolution enables us to explain the behaviour of entanglement in both deep quantum and semiclassical regimes for regular as well as chaotic regions. Hence, our analysis resolves the long-standing debates regarding the connection between classical chaos and quantum entanglement in deep quantum and semiclassical regimes. In addition to the study of entanglement, we perform the first study of nonlocality, and the effect of chaos on its generation in the QKT. Since nonlocality and entanglement are inequivalent quantum resources, the effect of chaos on nonlocality merits an explicit study. Violations of Bell inequalities in the presence of spacelike separation among the subsystems imply nonlocality - meaning nonlocal correlations between subsystems of the total spin system. We show that the QKT evolution can lead to states that violate multiqubit Bell inequalities and hence provides a deterministic method to prepare nonlocal quantum states. Our numerical results suggest a correlation between delocalized evolution of a pure quantum state and generation of nonlocality in the quantum state. We further demonstrate that dynamical tunnelling - a classically forbidden phenomenon - in the QKT leads to the generation of Greenberger-Horne-Zeilinger (GHZ)-like states for even numbers of qubits. We analytically prove that these states are maximally nonlocal. On the other hand, we numerically show that any reduced state of the QKT obtained by tracing out a subsystem of the total spin system does not violate Bell inequalities. We provide an analytical explanation of the numerical results for $2-$qubit reduced states by formulating and proving two general theorems regarding $2-$qubit Bell inequalities. These theorems imply that any $2-$qubit mixed state having a symmetric extension or symmetric purification cannot violate the Clauser-Horne-Shimony-Holt inequality. This highlights fundamental connections between two important and distinct concepts in quantum information science - Bell inequalities and symmetric extension of quantum states. Apart from providing deeper insights into the fundamental questions of quantum-classical correspondence and new approaches to analyze quantum chaos, the methods developed in this thesis can be used to design quantum systems that can efficiently generate entanglement and nonlocality. Thus, our results could have interesting applications in quantum computing and quantum information science.
Entanglement In Spin Chains
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Author : Abolfazl Bayat
language : en
Publisher: Springer Nature
Release Date : 2022-09-26
Entanglement In Spin Chains written by Abolfazl Bayat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-26 with Science categories.
This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.
An Introduction To Quantum Spin Systems
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Author : John B. Parkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-20
An Introduction To Quantum Spin Systems written by John B. Parkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-20 with Science categories.
The topic of lattice quantum spin systems is a fascinating and by now well established branch of theoretical physics. Based on a set of lectures, this book has a level of detail missing from others, and guides the reader through the fundamentals of the field.
Physics Of Quantum Information The Proceedings Of The 28th Solvay Conference On Physics
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Author : David J Gross
language : en
Publisher: World Scientific
Release Date : 2023-03-16
Physics Of Quantum Information The Proceedings Of The 28th Solvay Conference On Physics written by David J Gross and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-16 with Science categories.
Ever since 1911, the Solvay Conferences have shaped modern physics. The format is quite different from other conferences as the emphasis is placed on discussion. The 28th edition held in May 2022 in Brussels and chaired by David Gross and Peter Zoller continued this tradition and addressed some of the most pressing open questions in the fields of quantum information, gathering many of the leading figures working on a wide variety of profound problems.The proceedings contain the 'rapporteur talks' giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions: The Physics of Quantum Information, Many-Body Entanglement, Quantum Information and Spacetime, Quantum Platforms, Quantum Algorithms.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — expert, yet lively and sometimes contentious — have been edited to retain their flavor and are reproduced in full. The reader is taken on a breathtaking ride through a fascinating field which is expanding rapidly.
Selected Papers
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Author : Igor E. Tamm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Selected Papers written by Igor E. Tamm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
I.E. Tamm is one of the great figures of 20th century physics and the mentor of the late A.D. Sakharov. Together with I.M. Frank, he received the Nobel Prize in 1958 for the explanation of the Cherenkov effect. This book contains a commented selection of his most important contributions to the physical literature and essays on his contemporaries - Mandelstam, Einstein, Landau, and Bohr - as well as his contributions to Pugwash conferences. About a third of the selections originally appeared in Russian and are, to our knowledge, for the first time now available to Western readers. This volume includes a preface by Sir Rudolf Peierls, a biography compiled by Tamm's former students, V.Ya. Frenkel and B.M. Bolotovskii, and a complete bibliography.
Tensor Network Contractions
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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
Quantum Ising Phases And Transitions In Transverse Ising Models
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Author : Sei Suzuki
language : en
Publisher: Springer
Release Date : 2012-12-14
Quantum Ising Phases And Transitions In Transverse Ising Models written by Sei Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Science categories.
Quantum phase transitions, driven by quantum fluctuations, exhibit intriguing features offering the possibility of potentially new applications, e.g. in quantum information sciences. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area.
Manipulating Quantum Systems
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Author : National Academies of Sciences, Engineering, and Medicine
language : en
Publisher: National Academies Press
Release Date : 2020-10-14
Manipulating Quantum Systems written by National Academies of Sciences, Engineering, and Medicine and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-14 with Science categories.
The field of atomic, molecular, and optical (AMO) science underpins many technologies and continues to progress at an exciting pace for both scientific discoveries and technological innovations. AMO physics studies the fundamental building blocks of functioning matter to help advance the understanding of the universe. It is a foundational discipline within the physical sciences, relating to atoms and their constituents, to molecules, and to light at the quantum level. AMO physics combines fundamental research with practical application, coupling fundamental scientific discovery to rapidly evolving technological advances, innovation and commercialization. Due to the wide-reaching intellectual, societal, and economical impact of AMO, it is important to review recent advances and future opportunities in AMO physics. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States assesses opportunities in AMO science and technology over the coming decade. Key topics in this report include tools made of light; emerging phenomena from few- to many-body systems; the foundations of quantum information science and technologies; quantum dynamics in the time and frequency domains; precision and the nature of the universe, and the broader impact of AMO science.
Quantum Quenching Annealing And Computation
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Author : Anjan Kumar Chandra
language : en
Publisher: Springer
Release Date : 2010-07-23
Quantum Quenching Annealing And Computation written by Anjan Kumar Chandra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Science categories.
The process of realizing the ground state of some typical (frustrated) quantum many-body systems, starting from the ‘disordered’ or excited states, can be formally mapped to the search of solutions for computationally hard problems. The dynamics through the critical point, in between, are therefore extremely crucial. In the context of such computational optimization problems, the dynamics (of rapid quenching or slow annealing), while tuning the appropriate elds or uctuations, in particular while crossing the quantum critical point, are extremely intriguing and are being investigated these days intensively. Several successful methods and tricks are now well established. This volume gives a collection of introductory reviews on such developments written by well-known experts. It concentrates on quantum phase transitions and their dynamics as the transition or critical points are crossed. Both the quenching and annealing dynamics are extensively covered. We hope these timely reviews will inspire the young researchers to join and c- tribute to this fast-growing, intellectually challenging, as well as technologically demanding eld. We are extremely thankful to the contributors for their intensive work and pleasant cooperations. We are also very much indebted to Kausik Das for his help in compiling this book. Finally, we express our gratitude to Johannes Zittartz, Series Editor, LNP, and Christian Caron of physics editorial department of Springer for their encouragement and support.
The Physics Of Quantum Mechanics
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Author : James Binney
language : en
Publisher: Oxford University Press
Release Date : 2013-12
The Physics Of Quantum Mechanics written by James Binney and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12 with Science categories.
This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.