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)

References in corpus (16)

• Quantum Cryptography
• Experimental quantum teleportation
• A computable measure of entanglement
• Quantum error-correcting codes associated with graphs
• Separability Properties of Three-mode Gaussian States
• Estimating the spectrum of a density operator
• A uniqueness theorem for entanglement measures
• Achievable rates for the Gaussian quantum channel
• Distillability via protocols respecting the positivity of partial transpose
• Quantum Computing with Quantum Dots on Linear Supports
• Characterization of Distillable and Activable States using Entanglement Witnesses
• 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
• Bibliographic guide to the foundations of quantum mechanics and quantum information

Cited by in corpus (140)

• Quantum Information and Relativity Theory
• Quantum cloning
• Leggett-Garg Inequalities
• Concepts of quantum non-Markovianity: a hierarchy
• Quantum channels and memory effects
• Quantifying Entanglement with Witness Operators
• Quantum Channels with Memory
• Cold Bosons in Optical Lattices
• Quantum channels and their entropic characteristics
• Reexamination of Quantum Bit Commitment: the Possible and the Impossible
• Tema Con Variazioni: Quantum Channel Capacity
• Effects of symmetry breaking in finite quantum systems
• Quantum Black Holes: Entropy and Entanglement on the Horizon
• Ergodic and Mixing Quantum Channels in Finite Dimensions
• Coherence generating power of quantum unitary maps and beyond
• Contextual-value approach to the generalized measurement of observables
• Scheme of thinking quantum systems
• Operational distance and fidelity for quantum channels
• Distillability and positivity of partial transposes in general quantum field systems
• Transfer of an unknown quantum state, quantum networks, and memory
• Quantum Probabilities as Behavioral Probabilities
• The Generalized Lyapunov Theorem and its Application to Quantum Channels
• Entanglement Measure for Composite Systems
• Radon-Nikodym derivatives of quantum operations
• Fermionic systems for quantum information people
• Quantum capacity analysis of multi-level amplitude damping channels
• Quantifying Entanglement Production of Quantum Operations
• On quantum vs. classical probability
• Quantum internet using code division multiple access
• Extended Cahill and Glauber formalism for finite dimensional spaces II. Applications in quantum tomography and quantum teleportation
• The next stage: quantum game theory
• Decoherence and maximal violations of the Leggett-Garg inequality
• Witnessing incompatibility of quantum channels
• Quantum probabilities of composite events in quantum measurements with multimode states
• Types of quantum information
• Quasiparticle entanglement: redefinition of the vacuum and reduced density matrix approach
• Joint measurability of quantum effects and the matrix diamond
• Quantum decision making by social agents
• Evolutional Entanglement in Nonequilibrium Processes
• Regulating entanglement production in multitrap Bose-Einstein condensates
• Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State
• Causal evolution of wave packets
• Channel kets, entangled states, and the location of quantum information
• Is nonclassicality-breaking the same thing as entanglement-breaking?
• Decoherence and equilibration under nondestructive measurements
• Discrete squeezed states for finite-dimensional spaces
• Hilbert-space localization in closed quantum systems
• Stochastic resonance effects in quantum channels
• Quantum theory realises all joint measurability graphs
• Quantifying the noise of a quantum channel by noise addition
• Entanglement production with multimode Bose-Einstein condensates in optical lattices
• Quantum Optimal Transport
• There is more to quantum interferometry than entanglement
• Semantics for a Quantum Programming Language by Operator Algebras
• Programmability of covariant quantum channels
• Semantics and simulation of communication in quantum programming
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• The noncommutative geometry of Zitterbewegung
• The many classical faces of quantum structures
• Implementing generalized measurements with superconducting qubits
• A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective
• Quantumness and Entanglement Witnesses
• A complementarity-based approach to phase in finite-dimensional quantum systems
• Mode interference in quantum joint probabilities for multimode Bose-condensed systems
• Quantum Watermarking by Frequency of Error when Observing Qubits in Dissimilar Bases
• Compatibility of quantum measurements and inclusion constants for the matrix jewel
• A geometric Hamiltonian description of composite quantum systems and quantum entanglement
• Coherent dynamics of radiating atomic systems in pseudospin representation
• Reversible monadic computing
• Quantum probabilities and entanglement for multimode quantum systems
• Partially Coherent Direct Sum Channels
• Spectral Action in Noncommutative Geometry
• Universal quantum state merging
• Covariant quantum instruments
• Evolutional entanglement production
• Parametric separation of symmetric pure quantum states
• Qubit quantum channels: A characteristic function approach
• Order indices and entanglement production in quantum systems
• Role of collective information in networks of quantum operating agents
• Entanglement production with Bose atoms in optical lattices
• Entanglement production by statistical operators
• Optimal asymptotic cloning machines
• Blind encoding into qudits
• State determination: an iterative algorithm
• Entropy production rates of bistochastic strictly contractive quantum channels on a matrix algebra
• Representation of quantum states as points in a probability simplex associated to a SIC-POVM
• Dynamics of an Open System for Repeated Harmonic Perturbation
• Quantum Operation of Affective Artificial Intelligence
• Variational certification of quantum devices
• Tossing Quantum Coins and Dice
• The Stochastic-Quantum Correspondence
• Subsystems and Independence in Relativistic Microscopic Physics
• Strong subadditivity inequality for quantum entropies and four-particle entanglement
• Transmitting qudits through larger quantum channels
• Depolarization for quantum channels with higher symmetries
• Reduced dynamics with Poincaré symmetry in an open quantum system
• Categories of Quantum and Classical Channels
• Categories of Quantum and Classical Channels (extended abstract)
• Domains of commutative C*-subalgebras
• Superluminal local operations in quantum field theory: A ping-pong ball test
• Qubit entanglement in multimagnon states
• Linear programming with unitary-equivariant constraints
• Phase-covariant mixtures of non-unital qubit maps
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry
• Quantum compression relative to a set of measurements
• Positive maps, states, entanglement and all that; some old and new problems
• Entanglement production by evolution operator
• Quantum Field Measurements in the Fewster-Verch Framework
• Effectuses in Categorical Quantum Foundations
• Random covariant quantum channels
• The pitfalls of deciding whether a quantum channel is (conjugate) degradable and how to avoid them
• Quantum collapse rules from the maximum relative entropy principle
• Review of recent experimental progresses in Foundations of Quantum Mechanics and Quantum Information obtained in Parametric Down Conversion Experiments at IENGF
• A measurable entanglement criterion for two qubits
• Quantum Mechanics With Noncommutative Amplitudes
• Leggett-Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath
• Universal Asymmetric Quantum Cloning Revisited
• Quantum mappings acting by coordinate transformations on Wigner distributions
• An algebraic framework for information theory: Classical Information
• 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
• Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory
• Quantum system identification
• Some aspects of the interplay between bipartite correlations and quantum channels
• Quantum information theory and Fourier multipliers on quantum groups
• Positive operator-valued measures in quantum decision theory
• Spin Squeezing, Macrorealism and the Heisenberg uncertainty principle
• An algebraic approach to information theory
• Entanglement-assisted classical information capacity of the amplitude damping channel
• Three-Qubit Groverian Measure
• Entanglement - A Queer In The World Of Quantum : Some Perspectives