Fundamentals of Quantum Information Theory

Abstract

In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their mathematical description. The second part is focused on a presentation of the quantitative aspects of the theory. Topics discussed in this context include: entanglement measures, channel capacities, relations between both, additivity and continuity properties and asymptotic rates of quantum operations. Finally we give an overview on some recent developments and open questions.

118 Pages, LaTeX2e, 38 figures (19 eps, 19 ps-tricks)

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• Quantum error-correcting codes associated with graphs
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• On the von Neumann capacity of noisy quantum channels
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• Daylight quantum key distribution over 1.6 km
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• Estimating the spectrum of a density operator
• Practical quantum key distribution over a 48-km optical fiber network
• Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
• A uniqueness theorem for entanglement measures
• Optimal state estimation for d-dimensional quantum systems
• Optimal purification of single qubits
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• Characterization of Distillable and Activable States using Entanglement Witnesses
• Coupling nanocrystals to a high-$Q$ silica microsphere: entanglement in quantum dots via photon exchange
• The quantum capacity is properly defined without encodings
• Mixed-state entanglement and quantum communication
• Cloning and Cryptography with Quantum Continuous Variables
• Lower bound for the quantum capacity of a discrete memoryless quantum channel
• Quantum Information Theory - an Invitation
• Estimating mixed quantum states
• Bibliographic guide to the foundations of quantum mechanics and quantum information

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• Open-loop quantum control as a resource for secure communications
• An introduction to quantum coin-tossing
• Lindbladian-Induced Alignment in Quantum Measurements
• The Category-Theoretic Arithmetic of Information
• Preservation of entanglement in local noisy channels
• Inequivalent Vacuum States in Algebraic Quantum Theory
• Role of information in decision making of social agents
• A new approach to characterize qubit channels
• Algebras of infinite qubit systems
• One, Two, and $n$ Qubit Decoherence
• Constructing k-local parent Lindbladians for matrix product density operators
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• Entanglement - A Queer In The World Of Quantum : Some Perspectives