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" Elementary operators and their applications : "
Raúl E. Curto, Martin Mathieu, Editors.
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BL
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860762
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| Title & Author
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Quantum physics and geometry /\ editors Edoardo Ballico, Alessandra Bernardi, Iacopo Carusotto, Sonia Mazzucchi and Valter Moretti.
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| Publication Statement
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Cham, Switzerland :: S Springer,, [2019]
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, ©2019
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| Series Statement
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Lecture notes of the Unione Matematica Italiana ;; Volume 25
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1 online resource
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| ISBN
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3030061221
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: 303006123X
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: 9783030061227
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: 9783030061234
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3030061213
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9783030061210
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Includes bibliographical references.
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| Contents
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Intro; Contents; Contributors; 1 Introduction; References; 2 A Very Brief Introduction to Quantum Computing and Quantum Information Theory for Mathematicians; 2.1 Overview; 2.2 Quantum Computation as Generalized Probabilistic Computation; 2.2.1 Classical and Probabilistic Computing via Linear Algebra; 2.2.2 A Wish List; 2.2.3 Postulates of Quantum Mechanics and Relevant Linear Algebra; 2.3 Entanglement Phenomena; 2.3.1 Super-Dense Coding; 2.3.2 Quantum Teleportation; 2.3.3 Bell's Game; 2.3.3.1 Classical Version; 2.3.3.2 Quantum Version; 2.4 Quantum Algorithms; 2.4.1 Grover's Search Algorithm
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2.4.2 The Quantum Discrete Fourier Transform2.4.3 The Hidden Subgroup Problem; 2.5 Classical Information Theory; 2.5.1 Data Compression: Noiseless Channels; 2.5.2 Transmission over Noisy Channels; 2.5.2.1 Capacity of a Noisy Channel; 2.6 Reformulation of Quantum Mechanics; 2.6.1 Partial Measurements; 2.6.2 Mixing Classical and Quantum Probability; 2.6.3 Reformulation of the Postulates of Quantum Mechanics; 2.6.4 Expectation and the Uncertainty Principle; 2.6.5 Pure and Mixed States; 2.7 Communication Across a Quantum Channel; 2.8 More on von Neumann Entropy and Its Variants
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2.9 Entanglement and LOCC2.9.1 LOCC; 2.9.2 A Partial Order on Probability Distributions Compatible with Entropy; 2.9.3 A Reduction Theorem; 2.9.4 Entanglement Distillation (Concentration) and Dilution; 2.10 Tensor Network States; 2.11 Representation Theory in Quantum Information Theory; 2.11.1 Review of Relevant Representation Theory; 2.11.2 Quantum Marginals and Projections onto Isotypic Subspaces of H d; References; 3 Entanglement, CP-Maps and Quantum Communications; 3.1 Introduction; 3.2 Entanglement; 3.2.1 Quantum Correlations and EPR Paradox; 3.2.2 Sample of Separability Criteria
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3.3 Quantum Channels3.3.1 Completely Positive Maps; 3.3.2 Stinespring Representation; 3.3.3 Noisy Channels; 3.4 Quantum Communications; 3.4.1 Information Processing; 3.4.2 Relevant No-Go Theorems: Impossible Machines; 3.4.3 Quantum Teleportation; 3.4.4 Dense Coding; 3.5 Final Remarks and Perspectives; References; 4 Frontiers of Open Quantum System Dynamics; 4.1 Introduction; 4.2 Open Quantum System Dynamics; 4.3 Characterization of Dynamics with Memory; 4.3.1 Generalized Non-Markovianity Measure; 4.4 Non-Markovian Evolution Equations; 4.5 Conclusions and Outlook; References
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5 Geometric Constructions over C and F2 for Quantum Information5.1 Introduction; 5.2 The Geometry of Entanglement; 5.2.1 Entanglement Under SLOCC, Tensor Rank and Algebraic Geometry; 5.2.2 The Three-Qubit Classification via Auxiliary Varieties; 5.2.3 Geometry of Hyperplanes: The Dual Variety; 5.2.4 Representation Theory and Quantum Systems; 5.2.5 From Sequence of Simple Lie Algebras to the Classification of Tripartite Quantum Systems with Similar Classes of Entanglement; 5.3 The Geometry of Contextuality; 5.3.1 Observable-Based Proofs of Contextuality
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| Abstract
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This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics, which makes intense use of the most advanced concepts from each discipline. In each contribution, the authors give pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find new open challenges for their research. At the same time, the volume will also be of use to physicists wishing to learn advanced mathematical tools, especially those of a differential and algebraic geometric nature.
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Geometry.
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Quantum theory.
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Geometry.
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Quantum theory.
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SCIENCE-- Energy.
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SCIENCE-- Mechanics-- General.
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SCIENCE-- Physics-- General.
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| Dewey Classification
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530.12
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| LC Classification
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QC174.12
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| Added Entry
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Ballico, E., (Edoardo),1955-
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Bernardi, Alessandra
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Carusotto, Iacopo
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Mazzucchi, Sonia
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Moretti, Valter
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