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Author: Omar Fawzi Publisher: ISBN: Category : Languages : en Pages :
Book Description
"Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart of why some classically impossible cryptographic primitives become possible when quantum communication is allowed. This thesis is concerned with strong notions of uncertainty relations and their applications in quantum information theory.One operational manifestation of such uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. We give new efficient constructions of bases satisfying strong uncertainty relations leading to the first explicit construction of an informationlocking scheme. We also give several other applications of our uncertainty relations both to cryptographic and communication tasks.In addition, we define objects called QC-extractors, that can be seen as strong uncertainty relations that hold against quantum adversaries. We provide several constructions of QC-extractors, and use them to prove the security of cryptographic protocols for two-party computations based on the sole assumption that the parties' storage device is limited in transmitting quantum information. In doing so, we resolve a central question in the so-called noisy-storage model by relating security to the quantum capacity of storage devices." --
Author: Omar Fawzi Publisher: ISBN: Category : Languages : en Pages :
Book Description
"Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart of why some classically impossible cryptographic primitives become possible when quantum communication is allowed. This thesis is concerned with strong notions of uncertainty relations and their applications in quantum information theory.One operational manifestation of such uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. We give new efficient constructions of bases satisfying strong uncertainty relations leading to the first explicit construction of an informationlocking scheme. We also give several other applications of our uncertainty relations both to cryptographic and communication tasks.In addition, we define objects called QC-extractors, that can be seen as strong uncertainty relations that hold against quantum adversaries. We provide several constructions of QC-extractors, and use them to prove the security of cryptographic protocols for two-party computations based on the sole assumption that the parties' storage device is limited in transmitting quantum information. In doing so, we resolve a central question in the so-called noisy-storage model by relating security to the quantum capacity of storage devices." --
Author: Pedro W. Lamberti Publisher: MDPI ISBN: 3038977543 Category : Science Languages : en Pages : 188
Book Description
Since its conception 90 years ago, the quantum uncertainty principle introduced by Werner Heisenberg lies behind most important features of quantum physics, and its implications have an impact that goes far beyond the physics community. This book focuses on the quantum uncertainty principle, providing an up-to-date examination of recent developments of its applications in quantum information theory. The book brings together several renowned experts working in the foundations of quantum mechanics and quantum information theory. The authors provide different approaches to the study of uncertainty relations and other fundamental aspects of the quantum formalism. Topics addressed include entanglement and Bell inequalities, the application of entropic information measures to the study of uncertainty inequalities, the characterization of deep learning networks in the context of adiabatic quantum computation, and the study of general properties of the set of quantum states. The content of this book will surely benefit both experienced and new researchers specializing in quantum information theory and the foundations of quantum mechanics.
Author: Paolo Fornasini Publisher: Springer Science & Business Media ISBN: 0387786503 Category : Technology & Engineering Languages : en Pages : 291
Book Description
The scienti c method is based on the measurement of di erent physical qu- tities and the search for relations between their values. All measured values of physical quantities are, however, a ected by uncertainty. Understanding the origin of uncertainty, evaluating its extent, and suitably taking it into account in data analysis, are fundamental steps for assessing the global accuracy of physical laws and the degree of reliability of their technological applications. The introduction to uncertainty evaluation and data analysis procedures is generally made in laboratory courses for freshmen. During my long-lasting teaching experience, I had the feeling of some sort of gap between the ava- able tutorial textbooks, and the specialized monographs. The present work aims at lling this gap, and has been tested and modi ed through a feedback interaction with my students for several years. I have tried to maintain as much as possible a tutorial approach, that, starting from a phenomenolo- cal introduction, progressively leads to an accurate de nition of uncertainty and to some of the most common procedures of data analysis, facilitating the access to advanced monographs. This book is mainly addressed to - dergraduate students, but can be a useful reference for researchers and for secondary school teachers. The book is divided into three parts and a series of appendices. Part I is devoted to a phenomenological introduction to measurement and uncertainty. In Chap.
Author: Giovanni Battista Rossi Publisher: Springer ISBN: 9401788251 Category : Science Languages : en Pages : 288
Book Description
Measurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gathering information from the real world. Is it possible to develop a single theory of measurement for the various domains of science and technology in which measurement is involved? This book takes the challenge by addressing the following main issues: What is the meaning of measurement? How do we measure? What can be measured? A theoretical framework that could truly be shared by scientists in different fields, ranging from physics and engineering to psychology is developed. The future in fact will require greater collaboration between science and technology and between different sciences. Measurement, which played a key role in the birth of modern science, can act as an essential interdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems in measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation of inter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. Currently, increasing attention is paid to these issues due to their scientific, technical, economic and social impact. The book proposes a unified probabilistic approach to them which may allow more rational and effective solutions to be reached. Great care was taken to make the text as accessible as possible in several ways. Firstly, by giving preference to as interdisciplinary a terminology as possible; secondly, by carefully defining and discussing all key terms. This ensures that a wide readership, including people from different mathematical backgrounds and different understandings of measurement can all benefit from this work. Concerning mathematics, all the main results are preceded by intuitive discussions and illustrated by simple examples. Moreover, precise proofs are always included in order to enable the more demanding readers to make conscious and creative use of these ideas, and also to develop new ones. The book demonstrates that measurement, which is commonly understood to be a merely experimental matter, poses theoretical questions which are no less challenging than those arising in other, apparently more theoretical, disciplines.
Author: OpenStax Publisher: ISBN: 9781680920451 Category : Science Languages : en Pages : 622
Book Description
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.
Author: Simona Salicone Publisher: Springer ISBN: 331974139X Category : Mathematics Languages : en Pages : 327
Book Description
This monograph considers the evaluation and expression of measurement uncertainty within the mathematical framework of the Theory of Evidence. With a new perspective on the metrology science, the text paves the way for innovative applications in a wide range of areas. Building on Simona Salicone’s Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence, the material covers further developments of the Random Fuzzy Variable (RFV) approach to uncertainty and provides a more robust mathematical and metrological background to the combination of measurement results that leads to a more effective RFV combination method. While the first part of the book introduces measurement uncertainty, the Theory of Evidence, and fuzzy sets, the following parts bring together these concepts and derive an effective methodology for the evaluation and expression of measurement uncertainty. A supplementary downloadable program allows the readers to interact with the proposed approach by generating and combining RFVs through custom measurement functions. With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field.
Author: Vladimir B. Braginsky Publisher: Cambridge University Press ISBN: 9780521484138 Category : Science Languages : en Pages : 216
Book Description
This book is an up-to-date introduction to the quantum theory of measurement. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neuman, and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as "squeezed light," single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book begins with a brief introduction to the relevant theory and goes on to discuss all aspects of the design of practical quantum measurement systems.
Author: Omar Fawzi
Author: Omar Fawzi
Author: Dong Wang
Author: Pedro W. Lamberti
Author: Guido Tosello
Author: Paolo Fornasini
Author: Giovanni Battista Rossi
Author: S. Ishikawa
Author: OpenStax
Author: Simona Salicone
Author: Vladimir B. Braginsky