Symmetry, Asymmetry and Quantum Information

Symmetry, Asymmetry and Quantum Information

Author: Iman Marvian Mashhad

Publisher:

Published: 2012

Total Pages: 237

ISBN-13:

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It is impossible to overstate the importance of symmetry in physics and mathematics. Symmetry arguments play a central role in a broad range of problems from simplifying a system of linear equations to a deep role in organizing the fundamental principles of physics. They are used, for instance, in Noether's theorem to find the consequences of symmetry of a dynamics. For many systems of interest, the dynamics are sufficiently complicated that one cannot hope to characterize their evolution completely, whereas by appealing to the symmetries of the dynamical laws one can easily infer many useful results. In part I of this thesis we study the problem of finding the consequences of symmetry of a (possibly open) dynamics from an information-theoretic perspective. The study of this problem naturally leads us to the notion of asymmetry of quantum states. The asymmetry of a state relative to some symmetry group specifies how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful to constrain which final states of the system can be reached from a given initial state. Another motivation for the study of asymmetry comes from the field of quantum metrology and relatedly the field of quantum reference frames. It turns out that the degree of success one can achieve in many metrological tasks depends only on the asymmetry properties of the state used for metrology. We show that some ideas and tools developed in the field of quantum information theory are extremely useful to study the notion of asymmetry of states and therefore to find the consequences of symmetry of an open or closed system dynamics. In part II of this thesis we present a novel application of symmetry arguments in the field of quantum estimation theory. We consider a family of multi-copy estimation problems wherein one is given n copies of an unknown quantum state according to some prior distribution and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. We introduce a new approach to this problem by considering the symmetries of the prior and the symmetries of the parameters to be estimated. We show that based on these symmetries one can find strong constraints on the amount of entanglement required to implement the optimal measurement. In order to infer properties of the optimal estimation procedure from the symmetries of the parameters and the prior we come up with a generalization of Schur-Weyl duality. Just as Schur-Weyl duality has many applications to quantum information theory and quantum algorithms so too does this generalization. In this thesis we explore some of these applications.


Quantum Information and Symmetry

Quantum Information and Symmetry

Author: Wiesław Leoński

Publisher: MDPI

Published: 2020-06-03

Total Pages: 104

ISBN-13: 3039288008

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Recent research in the fields related to the quantum information theory (QIT) is becoming some of the most intriguing and promising investigations in contemporary physics. Many novel QIT concepts are discussed in the literature, and the broad range of new models of quantum optics and solid-state physics have been recently considered in the context of QIT. Theideas of symmetry are widely discussed in all physical sciences, becoming keystones of various concepts and considerations, leading to novel discoveries in physics. Thus, this Special Issue is devoted to the broad range of QIT topics that are related to the ideas of symmetry. It covers a broad range of ideas that can develop upon the basic research and applications in the field of quantum information, and in general, quantum theory.


Physical Origins of Time Asymmetry

Physical Origins of Time Asymmetry

Author: J. J. Halliwell

Publisher: Cambridge University Press

Published: 1996-03-21

Total Pages: 540

ISBN-13: 9780521568371

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We say that the processes going on in the world about us are asymmetric in time or display an arrow of time. Yet this manifest fact of our experience is particularly difficult to explain in terms of the fundamental laws of physics. This volume reconciles these profoundly conflicting facts.


Asymmetry: The Foundation of Information

Asymmetry: The Foundation of Information

Author: Scott J. Muller

Publisher: Springer Science & Business Media

Published: 2007-05-11

Total Pages: 174

ISBN-13: 3540698841

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This book gathers concepts of information across diverse fields –physics, electrical engineering and computational science – surveying current theories, discussing underlying notions of symmetry, and showing how the capacity of a system to distinguish itself relates to information. The author develops a formal methodology using group theory, leading to the application of Burnside's Lemma to count distinguishable states. This provides a tool to quantify complexity and information capacity in any physical system.


Quantum Symmetries

Quantum Symmetries

Author: Guillaume Aubrun

Publisher: Springer

Published: 2017-10-11

Total Pages: 126

ISBN-13: 331963206X

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Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.


Information Geometry and Its Applications

Information Geometry and Its Applications

Author: Nihat Ay

Publisher: Springer

Published: 2018-11-03

Total Pages: 450

ISBN-13: 3319977989

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The book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12–17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari’s 80th birthday and was organized by the Czech Academy of Sciences’ Institute of Information Theory and Automation. The conference received valuable financial support from the Max Planck Institute for Mathematics in the Sciences (Information Theory of Cognitive Systems Group), Czech Academy of Sciences’ Institute of Information Theory and Automation, and Università degli Studi di Roma Tor Vergata. The aim of the conference was to highlight recent advances in the field of information geometry and to identify new research directions. To this end, the event brought together leading experts in the field who, in invited talks and poster sessions, discussed both theoretical work and achievements in the many fields of application in which information geometry plays an essential role.


ULTIMATE SYMMETRY

ULTIMATE SYMMETRY

Author: Mohamed Haj Yousef

Publisher: Mohamed Haj Yousef

Published: 2019-01-01

Total Pages: 320

ISBN-13: 1723828696

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This is the third volume in the Single Monad Model of the Cosmos series. The second volume introduced the Duality of Time Theory, which provided elegant solutions to many persisting problems in physics and cosmology, including super-symmetry and matter-antimatter asymmetry. In addition to uniting the principles of Relativity and Quantum theories, this theory can also explain the psychical and spiritual domains; all based on the same discrete complex-time geometry. Super-symmetry, and quantum gravity, are realized only with the two complementary physical and psychical worlds, while the spiritual realm is governed by hyper-symmetry, which mirrors the previous two levels together, and all these three realms mirror the ultimate level of absolute oneness that describes the symmetry of the divine presence of God and His Beautiful Names and Attributes. This "ULTIMATE SYMMETRY" is a modern scientific account of the same ancient mystical, and greatly controversial, theory of the "Oneness of Being" that is often misinterpreted in terms of "pantheism", but it is indeed the concluding gnostic knowledge of God and creation. Otherwise, how can we understand the origin of the cosmos, with both or either of its corporeal and incorporeal realms, without referring to its Originator! In the literal sense, ultimate or perfect symmetry may seem to be trivial, because it means that all possible transformations in such a symmetric system are invariant. The system we are talking about here is the whole Universe that we are watching and experiencing its immense and sometimes shattering changes every moment of time. Yet many great philosophers, such as Parmenides and Ibn al-Arabi, maintained their firm belief that reality is unchanging One and existence is timeless and uniform, while all apparent changes are mere illusions induced by or in our sensory faculties. Nevertheless, since we are living inside it, this illusion is as good as reality for us. Therefore, we still need to explain how the Universe is being formulated. Only when are able to transcend beyond the current chest of time, we shall discover that we were living a dream, and we shall be able to see the whole Universe as unchanging symmetry. The Single Monad Model and the resulting Duality of Time Theory provide the link between this apparent dynamic multiplicity of creation and the ultimate metaphysical oneness. In fact, the complex-time geometry concludes that we are imagining the reality because we are observing it from a genuinely imaginary time dimension. Since the ultimate reality is One, we cannot view it from outside, because there is none! Thus, as we quoted in the Introduction, in the Book of Theophanies, Ibn al-Arabi ascribes to God as saying: Listen, O My beloved! I am the conclusive entity of the World. I am the center of the circle (of existence) and its circumference. I am its simple point and its compound whole. I am the Word descending between heaven and earth. I have created perceptions for you only to perceive Me. If you then perceive Me, you perceive yourself. But don't ever crave to perceive Me through yourself! It is through My Eyes that you see Me and see yourself. But through your own eyes you can never see Me! This Theophany of Perfection summarizes the Ultimate Symmetry between the single point and the encompassing space. It also summarizes the instantaneous process of creation, or re-creation, which is breaking this symmetry into the two arrows of time, that produce particles and anti-particles, and then restoring it through each subsequent annihilation. This reunion is also the fundamental cause of motion, which is formulated as the Principle of Love that leads to the stationary action that is the initial assumption of most physics theories including Relativity and Quantum Field theories.


Symmetries in Quantum Physics

Symmetries in Quantum Physics

Author: U. Fano

Publisher: Elsevier

Published: 1996-06-17

Total Pages: 349

ISBN-13: 0080542174

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This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, including the Wigner and Racah algebras and their applications to various symmetry groups. The book also includes some of the latest research on the use of non-invariance and non-compact groups in the consideration of relativistic and many-particle problems of atoms and nuclei. This book is an updated replacement for the text Irreducible Tensorial Sets (Academic Press, 1959). Parts A and B of the present book grew out of occasional lectures in the intervening decades at the University of Chicago, where it became neccessary to update or elaborate upon certain points. Part C has been built more recently to deal with innovations and new information in the field of mathematical physics. The book as a whole develops the subject of symmetry from a physical point of view, allowing students and researchers to gain new insight on their subject. This book can be used both as a text and as a reference by students and scientists in the field. Adapts and extends the earlier Irreducible Tensor Sets (Academic Press, 1959) to classroom use Extends to multi-particle systems and relativity Includes problems in each chapter for homework assignments Embraces the latest research on non-invariance groups


Symmetries in Quantum Mechanics

Symmetries in Quantum Mechanics

Author: G Jordan Maclay

Publisher: Mdpi AG

Published: 2022-01-07

Total Pages: 324

ISBN-13: 9783036526942

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Symmetry and quantum mechanics are two of the most fundamental probes we have of nature. This collection of eleven papers discusses new quantum phenomena in atoms, galaxies, and people (quantum cognition), which is a testimonial to the breadth of the influence of symmetry and quantum mechanics. The papers can be divided into four broad categories: 1. Fundamentals of quantum systems, including a new derivation of the uncertainty principle from optimal stochastic control theory, a new model of energy transfer between atoms with no wave function collapse, a new asymmetric optical micro-device with the remarkable property of showing a current with no applied voltage, a group theory method to compute radiative shifts, and a model of quantum cognition to predict the effect of irrelevant information on decision making, 2. Algebraic methods in quantum mechanics, applied for the elegant derivation of hydrogen atom Stark effect matrix elements and a group theoretical method for the computation of radiative shifts, 3. Teleportation and scattering, including a method to improve the information transfer in teleportation and the use of permutation symmetry to compute scattering cross sections, and 4. Cosmology, including scalar-tensor theory applied to inflation, the characterization of new Levi-Cevita spacetimes, and the analysis of gravitational dispersion forces. The book represents an international effort of researchers from educational and research institutions in nine countries, including India, Finland, France, Mexico, Norway, Russia, Spain, Turkey, and the United States.