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000866143 019__ $$a1090171764$$a1090368274$$a1091245745
000866143 020__ $$a9783030061227$$q(electronic book)
000866143 020__ $$a3030061221$$q(electronic book)
000866143 020__ $$z9783030061210
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000866143 0247_ $$a10.1007/978-3-030-06122-7$$2doi
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000866143 049__ $$aISEA
000866143 050_4 $$aQC174.12
000866143 08204 $$a530.12$$223
000866143 24500 $$aQuantum physics and geometry /$$ceditors Edoardo Ballico, Alessandra Bernardi, Iacopo Carusotto, Sonia Mazzucchi and Valter Moretti.
000866143 264_1 $$aCham, Switzerland :$$bs Springer,$$c[2019]
000866143 264_4 $$c©2019
000866143 300__ $$a1 online resource.
000866143 336__ $$atext$$btxt$$2rdacontent
000866143 337__ $$acomputer$$bc$$2rdamedia
000866143 338__ $$aonline resource$$bcr$$2rdacarrier
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000866143 4901_ $$aLecture notes of the Unione Matematica Italiana ;$$vVolume 25
000866143 504__ $$aIncludes bibliographical references.
000866143 5050_ $$aIntro; 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
000866143 5058_ $$a2.4.2 The Quantum Discrete Fourier Transform2.4.3 The Hidden Subgroup Problem; 2.5 Classical Information Theory; 2.5.1 Data Compression: Noiseless Channels; 2.5.2 Transmission over Noisy Channels; 2.5.2.1 Capacity of a Noisy Channel; 2.6 Reformulation of Quantum Mechanics; 2.6.1 Partial Measurements; 2.6.2 Mixing Classical and Quantum Probability; 2.6.3 Reformulation of the Postulates of Quantum Mechanics; 2.6.4 Expectation and the Uncertainty Principle; 2.6.5 Pure and Mixed States; 2.7 Communication Across a Quantum Channel; 2.8 More on von Neumann Entropy and Its Variants
000866143 5058_ $$a2.9 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
000866143 5058_ $$a3.3 Quantum Channels3.3.1 Completely Positive Maps; 3.3.2 Stinespring Representation; 3.3.3 Noisy Channels; 3.4 Quantum Communications; 3.4.1 Information Processing; 3.4.2 Relevant No-Go Theorems: Impossible Machines; 3.4.3 Quantum Teleportation; 3.4.4 Dense Coding; 3.5 Final Remarks and Perspectives; References; 4 Frontiers of Open Quantum System Dynamics; 4.1 Introduction; 4.2 Open Quantum System Dynamics; 4.3 Characterization of Dynamics with Memory; 4.3.1 Generalized Non-Markovianity Measure; 4.4 Non-Markovian Evolution Equations; 4.5 Conclusions and Outlook; References
000866143 5058_ $$a5 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
000866143 506__ $$aAccess limited to authorized users.
000866143 520__ $$aThis 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.
000866143 588__ $$aVendor-supplied metadata.
000866143 650_0 $$aQuantum theory.
000866143 650_0 $$aGeometry.
000866143 7001_ $$aBallico, E.$$q(Edoardo),$$d1955-$$eeditor.
000866143 7001_ $$aBernardi, Alessandra,$$eeditor.
000866143 7001_ $$aCarusotto, Iacopo,$$eeditor.
000866143 7001_ $$aMazzucchi, Sonia,$$eeditor.
000866143 7001_ $$aMoretti, Valter,$$eeditor.
000866143 77608 $$iPrint version: $$z3030061213$$z9783030061210$$w(OCoLC)1067249473
000866143 830_0 $$aLecture notes of the Unione Matematica Italiana ;$$v25.
000866143 852__ $$bebk
000866143 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-06122-7$$zOnline Access$$91397441.1
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