Quantum Correlations, Quantum Resource Theories and Exclusion Game

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Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (929 download)

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Book Synopsis Quantum Correlations, Quantum Resource Theories and Exclusion Game by : Zi-Wen Liu

Download or read book Quantum Correlations, Quantum Resource Theories and Exclusion Game written by Zi-Wen Liu and published by . This book was released on 2015 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses two topics in quantum information theory. The first topic is quantum correlations and quantum resource theory. The second is quantum communication theory. The first part summarizes an ongoing work about quantum correlations beyond entanglement and quantum resource theories. We systematically explain the concept quantum correlations beyond entanglement, and introduce a unified framework of measuring such correlations with entropic quantities. In particular, a new measure called Diagonal Discord (DD), which is simpler to compute than discord but still possesses several nice properties, is proposed. As an application to real physical scenarios, we study the scaling behaviors of quantum correlations in spin lattices with these measures. On its own, however, the theory of quantum correlations is not yet a satisfactory quantum resource theory. Some partial results towards this goal are introduced. Furthermore, a unified abstract structure of general quantum resource theories and its duality is formalized. The second part shows that there exist (one-way) communication tasks with an infinite gap between quantum communication complexity and quantum information complexity. We consider the exclusion game, recently introduced by Perry, Jain and Oppenheim [80], which exhibits the property that for appropriately chosen parameters of the game, there exists an winning quantum strategy that reveals vanishingly small amount of information as the size of the problem n increases, i.e., the quantum (internal) information cost vanishes in the large n limit. For those parameters, we prove the quantum communication cost (the size of quantum communication to succeed) is lower bounded by Q (log n), thereby proving an infinite gap between quantum information and communication costs. This infinite gap is further shown to be robust against sufficiently small error. Some other interesting features of the exclusion game are also discovered as byproducts.

Quantum Correlations

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Publisher : Springer
ISBN 13 : 3030241203
Total Pages : 166 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Quantum Correlations by : Farid Shahandeh

Download or read book Quantum Correlations written by Farid Shahandeh and published by Springer. This book was released on 2019-08-02 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correlations between physical systems provide significant information about their collective behaviour – information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated ‘resource’ is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.

Entanglement and Non Local Correlations: Quantum Resources for Information Processing

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ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Entanglement and Non Local Correlations: Quantum Resources for Information Processing by : Giuseppe Prettico

Download or read book Entanglement and Non Local Correlations: Quantum Resources for Information Processing written by Giuseppe Prettico and published by . This book was released on 2013 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Information Theory (QIT) studies how information can be processed and transmitted when encoded on quantum states. Practically, it can be understood as the effort to generalize Classical Information Theory to the quantum world. Interestingly, the fact that very-small scale Physics differs considerably from that of macroscopic objects offers a richer structure to the new theory. Among other phenomena, entanglement is at the heart of many quantum information protocols. It is the most spectacular and counter-intuitive manifestation of quantum mechanics: it signifies the existence of non-local correlations. Although intrinsically non-intuitive, these strange effects have been shown to lead to intriguing applications with no classical analogue. The main scope of this thesis is to establish qualitative and quantitative connections among the different quantum and classical information resources. Among the many weird effects that quantum systems present, the non-additivity concept plays an important role. In the quantum realm, the joint processing of two quantum resources is often better than the sum of the two resources. Activation is the strongest manifestation of non-additivity. It can be understood as the capability of two objects to achieve a given task that is impossible for each of them when considered individually. From a classical point of view, it is unknown whether such a process can hold. Here we focus on the classical secret-key rate. We provide two probability distributions conjectured to have bound information, hence from which it is conjectured that no secret key can be extracted when taken individually, but that lead to a positive secret-key rate when combined. For that, we exploit the close connection between the information-theoretic key agreement and the quantum entanglement scenario. Successively, we move to the multipartite scenario showing a one-to-one correspondence between bound information and bound entanglement. We provide an example of multipartite bound information which shares the same features of its quantum analogue, the Smolin state. Later, we move to prove a deep connection between privacy and non-locality. We do it by showing that all private states violate the Bell-CHSH inequality. Private states are those entangled states from which a perfectly secure cryptographic key can be extracted. An example of those is the maximally entangled state. But still, there are other private states that are not maximally entangled. While a maximally entangled state violates a Bell's inequality, this is not known a priori for the whole set. We give a general proof valid for any dimension and any number of parties. Private states, then, not only represent the unit of quantum privacy, but also allow two distant parties to establish a different quantum resource, namely non-local correlations. Lastly, we tackle the connection between non-locality and genuine randomness. Non-locality and genuine intrinsic randomness have been the subject of active interest since the early days of quantum physics. Initially, this interest was mainly derived from their foundational and fundamental implications but recently it also has acquired a practical aspect. Recent development in device independent scenario have heightened the need to quantify both the randomness and non-locality inherent in quantum systems. While some works try to deepen this relation, we provide a simple method to detect Bell tests that allow the certification of maximal randomness. These arguments exploit the symmetries of Bell inequalities and assume the uniqueness of the quantum probability distribution maximally violating it. We show how these arguments can be applied to intuit the randomness intrinsic in a probability distribution without resorting to numerical calculations.

The Role of Quantumness of Correlations in Entanglement Resource Theory

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis The Role of Quantumness of Correlations in Entanglement Resource Theory by : Tiago Debarba

Download or read book The Role of Quantumness of Correlations in Entanglement Resource Theory written by Tiago Debarba and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum correlations: entanglement and quantumness of correlations are main resource for quantum information theory. In this chapter, the scenarios which quantumness of correlations plays an interesting role in entanglement distillation protocol are presented. By means of Koashi-Winter relation, it is discussed that quantumness of correlations are related to the irreversibility of the entanglement distillation protocol. The activation protocol is introduced, and it is proved that quantumness of correlations can create distillable entanglement between the system and the measurement apparatus during a local measurement process.

Non-Local Correlations and Interactive Games

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Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (769 download)

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Book Synopsis Non-Local Correlations and Interactive Games by : Daniel Ciprian Preda

Download or read book Non-Local Correlations and Interactive Games written by Daniel Ciprian Preda and published by . This book was released on 2011 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum entanglement, and the resulting peculiar non-classical correlations are one of the most counter-intuitive aspects of quantum mechanics. The formalism of interactive games from computational complexity theory provides a useful framework in which to understand the power of entanglement. In an interactive game, a verifier interacts with a number of infinitely powerful provers who are allowed to share quantum entanglement but otherwise can't communicate. The ability of the verifier to extract useful information from the provers, whom he does not trust, provides an interesting measure of the ability of the provers to coordinate using their shared entanglement. Two particular interactive games we'll look at are Magic Square and 3SAT. The Magic Square game is the iconic example of a game where two classical provers cannot perfectly coordinate their strategies using shared randomness, but quantum provers with shared entanglement can win with probability 1. We show that by adding an extra prover, we disallow perfect cheating. For 3SAT with three provers we also show that perfect cheating is not possible. We then generalize the results for Magic Square and 3SAT by looking at non-commuting provers, a superset of entangled provers (communication is allowed, but operators applied by different provers must commute). Using this method, we obtain a generalized Tsirelson inequality that we apply to the Magic Square. Hence, we are able to give provably optimal strategies for the general Magic Square with n players. We also recover a similar result for 3SAT as with entangled provers, and we improve on it by showing that the gap is inverse exponential in the input size. The no-signaling principle, which forbids faster than light communication, is a fundamental constraint on the non-local correlations resulting from quantum entanglement. However, no-signaling allows distributions that are more general than those arising from quantum mechanics. In particular, using a specific "unit" of general non-local correlation (the Popescu-Rohlich box), we show that there are classes that are equal to NEXP classically, but collapse to AM once such correlations are allowed. We also show that MIP where the verifier only looks at the XOR of the answers collapses to PSPACE. For the second approach, we show that by writing general non-local correlations as linear constraints, MIP is included in EXP under such correlations (vs NEXP classically). We can extend these results to entangled quantum provers, by formulating an artificial MIP-like class built on a promise problem, that classically is equal to NEXP, but that also collapses to AM when quantum correlations are present.

The Role of Quantum Correlations Beyond Entanglement in Quantum Information Theory

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis The Role of Quantum Correlations Beyond Entanglement in Quantum Information Theory by : Alexander Streltsov

Download or read book The Role of Quantum Correlations Beyond Entanglement in Quantum Information Theory written by Alexander Streltsov and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Correlations and Informatin [sic] Theory

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ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.:/5 (83 download)

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Book Synopsis Quantum Correlations and Informatin [sic] Theory by : Lluís Masanes Meruelo

Download or read book Quantum Correlations and Informatin [sic] Theory written by Lluís Masanes Meruelo and published by . This book was released on 2004 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Many-Particle Entanglement, Einstein-Podolsky-Rosen Steering and Bell Correlations in Bose-Einstein Condensates

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Publisher : Springer Nature
ISBN 13 : 3030854728
Total Pages : 191 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Many-Particle Entanglement, Einstein-Podolsky-Rosen Steering and Bell Correlations in Bose-Einstein Condensates by : Matteo Fadel

Download or read book Many-Particle Entanglement, Einstein-Podolsky-Rosen Steering and Bell Correlations in Bose-Einstein Condensates written by Matteo Fadel and published by Springer Nature. This book was released on 2021-10-04 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents theoretical methods and experimental results on the study of multipartite quantum correlations in spin-squeezed Bose–Einstein condensates. Nonclassical correlations in many-body system​s are particularly interesting for both fundamental research and practical applications. For their investigation, ultracold atomic ensembles offer an ideal platform, due to their high controllability and long coherence times. In particular, we introduce criteria for detecting and characterizing multipartite entanglement, Einstein–Podolsky–Rosen steering, and Bell correlations. Moreover, we present the experimental observation of such correlations in systems of about 600 atoms.

Trends in Quantum Computing Research

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Publisher : Nova Publishers
ISBN 13 : 9781594548406
Total Pages : 264 pages
Book Rating : 4.5/5 (484 download)

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Book Synopsis Trends in Quantum Computing Research by : Susan Shannon

Download or read book Trends in Quantum Computing Research written by Susan Shannon and published by Nova Publishers. This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information processing is an exciting new emergent and interdisciplinary field. It combines questions of national security (When will today's public key cryptography be broken?) to questions of fundamental science (What are the fundamental limits to information processing?). It has thrived through the collaboration between the computer, engineering, mathematical and physical sciences. It is a field that is challenging our understanding of information, communication, computation, and of the fundamental laws of nature. This book brings together leading research in the field.

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

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Publisher : Springer
ISBN 13 : 9783319495705
Total Pages : 0 pages
Book Rating : 4.4/5 (957 download)

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Book Synopsis Characterizing Entanglement and Quantum Correlations Constrained by Symmetry by : Jordi Tura i Brugués

Download or read book Characterizing Entanglement and Quantum Correlations Constrained by Symmetry written by Jordi Tura i Brugués and published by Springer. This book was released on 2016-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.

Applications of Quantum Mechanical Techniques to Areas Outside of Quantum Mechanics. 2nd Edition

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Publisher : Frontiers Media SA
ISBN 13 : 2889631508
Total Pages : 164 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Applications of Quantum Mechanical Techniques to Areas Outside of Quantum Mechanics. 2nd Edition by : Emmanuel Haven

Download or read book Applications of Quantum Mechanical Techniques to Areas Outside of Quantum Mechanics. 2nd Edition written by Emmanuel Haven and published by Frontiers Media SA. This book was released on 2019-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950’s on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is ‘quantum probability’ and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test ‘non-rational’ decision making behaviour, one can observe that such data often exhibits a complex non-commutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantum-like models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world’s leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.

The Many-Worlds Interpretation of Quantum Mechanics

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Publisher : Princeton University Press
ISBN 13 : 140086805X
Total Pages : 264 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Many-Worlds Interpretation of Quantum Mechanics by : Bryce Seligman Dewitt

Download or read book The Many-Worlds Interpretation of Quantum Mechanics written by Bryce Seligman Dewitt and published by Princeton University Press. This book was released on 2015-03-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. In his interpretation, Dr. Everett denies the existence of a separate classical realm and asserts the propriety of considering a state vector for the whole universe. Because this state vector never collapses, reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality customarily perceived; rather, it is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables, the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result, and in most of which the familiar statistical quantum laws hold. The volume contains Dr. Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics," and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function," never before published. In addition, other papers by Wheeler, DeWitt, Graham, and Cooper and Van Vechten provide further discussion of the same theme. Together, they constitute virtually the entire world output of scholarly commentary on the Everett interpretation. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Theory Of Critical Phenomena In Finite-size Systems: Scaling And Quantum Effects

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Publisher : World Scientific
ISBN 13 : 9814494569
Total Pages : 459 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Theory Of Critical Phenomena In Finite-size Systems: Scaling And Quantum Effects by : Jordan G Brankov

Download or read book Theory Of Critical Phenomena In Finite-size Systems: Scaling And Quantum Effects written by Jordan G Brankov and published by World Scientific. This book was released on 2000-08-21 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems.The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.

Lectures on General Quantum Correlations and their Applications

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Publisher : Springer
ISBN 13 : 3319534122
Total Pages : 534 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Lectures on General Quantum Correlations and their Applications by : Felipe Fernandes Fanchini

Download or read book Lectures on General Quantum Correlations and their Applications written by Felipe Fernandes Fanchini and published by Springer. This book was released on 2017-06-24 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a distinctive way of understanding quantum correlations beyond entanglement, introducing readers to this less explored yet very fundamental aspect of quantum theory. It takes into account most of the new ideas involving quantum phenomena, resources, and applications without entanglement, both from a theoretical and an experimental point of view. This book serves as a reference for both beginner students and experienced researchers in physics and applied mathematics, with an interest in joining this novel venture towards understanding the quantum nature of the world.

Quantum Machine Learning

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Publisher : Academic Press
ISBN 13 : 0128010991
Total Pages : 176 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Quantum Machine Learning by : Peter Wittek

Download or read book Quantum Machine Learning written by Peter Wittek and published by Academic Press. This book was released on 2014-09-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine Learning sets the scene for a deeper understanding of the subject for readers of different backgrounds. The author has carefully constructed a clear comparison of classical learning algorithms and their quantum counterparts, thus making differences in computational complexity and learning performance apparent. This book synthesizes of a broad array of research into a manageable and concise presentation, with practical examples and applications. - Bridges the gap between abstract developments in quantum computing with the applied research on machine learning - Provides the theoretical minimum of machine learning, quantum mechanics, and quantum computing - Gives step-by-step guidance to a broader understanding of this emergent interdisciplinary body of research

Encyclopaedia of Mathematics, Supplement III

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Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Technology and Mathematics

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Publisher : Springer
ISBN 13 : 3319937790
Total Pages : 373 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Technology and Mathematics by : Sven Ove Hansson

Download or read book Technology and Mathematics written by Sven Ove Hansson and published by Springer. This book was released on 2018-10-24 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.