From Classical to Quantum Shannon Theory

Abstract

The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.

v8: 774 pages, 301 exercises, 81 figures, several corrections; this draft, pre-publication copy is available under a Creative Commons Attribution-NonCommercial-ShareAlike license (see http://creativecommons.org/licenses/by-nc-sa/3.0/), "Quantum Information Theory, Second Edition" is available for purchase from Cambridge University Press

Cited by in corpus (290)

• Quantum Resource Theories
• Non-Markovian quantum processes: complete framework and efficient characterisation
• A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
• Nearly optimal lattice simulation by product formulas
• Planckian dissipation, minimal viscosity and the transport in cuprate strange metals
• Coherence effects in the performance of the quantum Otto heat engine
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• One-shot coherence distillation
• Variational Quantum Fidelity Estimation
• Approaches for approximate additivity of the Holevo information of quantum channels
• A Mini-Introduction To Information Theory
• Time-dependent Hamiltonian simulation with $L^1$-norm scaling
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Machine learning non-Markovian quantum dynamics
• Convex geometry of quantum resource quantification
• Unifying Quantum and Classical Speed Limits on Observables
• The Quantum Wasserstein Distance of Order 1
• Practical figures of merit and thresholds for entanglement distribution in quantum networks
• Resource theory of asymmetric distinguishability for quantum channels
• The minimum error probability of quantum illumination
• Quantum algorithm for Petz recovery channels and pretty good measurements
• Quantum Limits in Optical Communications
• Scrambling is Necessary but Not Sufficient for Chaos
• Quantum coding with low-depth random circuits
• Cost of quantum entanglement simplified
• Quantum optimal transport with quantum channels
• A multipartite generalization of quantum discord
• Dynamical Entanglement
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Resource theory of asymmetric distinguishability
• From time-reversal symmetry to quantum Bayes' rules
• Noise-Assisted Quantum Autoencoder
• Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
• Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
• EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
• Entanglement cost and quantum channel simulation
• Tight bound on finite-resolution quantum thermometry at low temperatures
• Entropic uncertainty relations for quantum information scrambling
• Detecting and quantifying entanglement on near-term quantum devices
• Exact solution of time-dependent Lindblad equations with closed algebras
• Optimized quantum f-divergences and data processing
• Operational quantification of continuous-variable quantum resources
• Practical distributed quantum information processing with LOCCNet
• Operational Characterization of Divisibility of Dynamical Maps
• Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology
• Quantum capacity analysis of multi-level amplitude damping channels
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Applications of position-based coding to classical communication over quantum channels
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• Experimental characterisation of a non-Markovian quantum process
• Quantum Sequential Hypothesis Testing
• Tailored XZZX codes for biased noise
• Measuring Quantum Entropy
• Strong unitary and overlap uncertainty relations: theory and experiment
• Ruling out higher-order interference from purity principles
• Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels
• Quantum many-body systems in thermal equilibrium
• Estimating distinguishability measures on quantum computers
• Computing Quantum Channel Capacities
• Exact solution for the quantum and private capacities of bosonic dephasing channels
• Large-Scale Simulation of Shor's Quantum Factoring Algorithm
• Covert Capacity of Bosonic Channels
• The conditional Entropy Power Inequality for bosonic quantum systems
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Causal order as a resource for quantum communication
• Classical capacities of quantum channels with environment assistance
• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Generating steady quantum coherence and magic through an autonomous thermodynamic machine by utilizing a spin bath
• Positivity and nonadditivity of quantum capacities using generalized erasure channels
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Steering-enhanced quantum metrology using superpositions of noisy phase shifts
• Resource theory of quantum uncomplexity
• Quantum parameter estimation on coherently superposed noisy channels
• Optimal Extensions of Resource Measures and their Applications
• Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
• Entanglement-assisted private communication over quantum broadcast channels
• $\alpha$-Logarithmic negativity
• Experimental Demonstration of Quantum Pseudotelepathy
• Secure and Robust Identification via Classical-Quantum Channels
• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• On the mixed-unitary rank of quantum channels
• Magic Resources of the Heisenberg Picture
• Conditional quantum one-time pad
• Optimal Frobenius light cone in spin chains with power-law interactions
• Entropic singularities give rise to quantum transmission
• Emerging dynamics arising from coarse-grained quantum systems
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls
• Continuity of quantum entropic quantities via almost convexity
• Holevo Capacity of Discrete Weyl Channels
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Pursuing the fundamental limits for quantum communication
• Quantum Work Capacitances: ultimate limits for energy extraction on noisy quantum batteries
• Restoring quantum communication efficiency over high loss optical fibres
• Relativistic quantum communication between harmonic oscillator detectors
• Quantum secure two party computation for set intersection with rational players
• Multi-object operational tasks for convex quantum resource theories
• Data processing for the sandwiched Rényi divergence: a condition for equality
• Properties of Noncommutative Renyi and Augustin Information
• Quantum-Enhanced Transmittance Sensing
• Scrambling and Many-Body Localization in the XXZ-Chain
• Consequences of preserving reversibility in quantum superchannels
• Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
• Beyond Density Matrices: Geometric Quantum States
• Estimating Quantum Mutual Information Through a Quantum Neural Network
• How much entanglement can be created in a closed system?
• Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
• A family of permutationally invariant quantum codes
• The Near-optimal Performance of Quantum Error Correction Codes
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions
• Quantum Neural Estimation of Entropies
• Superadditivity of quantum relative entropy for general states
• Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels
• Activation and superactivation of single-mode Gaussian quantum channels
• Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum
• Epsilon-smooth measure of coherence
• One-shot quantum error correction of classical and quantum information
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Geometric aspects of analog quantum search evolutions
• Entanglement and thermalization
• Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities
• Emergent classicality in general multipartite states and channels
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors
• Qubit noise deconvolution
• Fluctuation-dissipation relations for thermodynamic distillation processes
• Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
• Quantum game theory and the complexity of approximating quantum Nash equilibria
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
• The Uncertainty Principle of Quantum Processes
• Quantum master equations for a system interacting with quantum gas in the low density limit and for the semiclassical collision model
• The platypus of the quantum channel zoo
• Horizon entanglement area law from regular black hole thermodynamics
• Control of the $ZZ$ coupling between Kerr-cat qubits via transmon couplers
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• Quantum metrology in the finite-sample regime
• Coherent-state constellations and polar codes for thermal Gaussian channels
• A-unital Operations and Quantum Conditional Entropy
• Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• Resonant Multilevel Amplitude Damping Channels
• Unravelling Metastable Markovian Open Quantum Systems
• On the optimal error exponents for classical and quantum antidistinguishability
• Dynamic generation of GHZ states with coupled charge qubits
• Quantum rebound capacity
• High-dimensional quantum encoding via photon-subtracted squeezed states
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• Quantum Channel Capacities Per Unit Cost
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Quantum outage probability for time-varying quantum channels
• Quantum discords of tripartite quantum systems
• High-fidelity, multi-qubit generalized measurements with dynamic circuits
• The effects of different quantum feedback operator types on the parameter precision of detection efficiency in optimal quantum estimation
• Temperley-Lieb quantum channels
• Estimating the Shannon entropy and (un)certainty relations for design-structured POVMs
• Maxwell's two-demon engine under pure dephasing noise
• Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices
• Partially Coherent Direct Sum Channels
• Quantum Optical Communication in the presence of strong attenuation noise
• Classical communication through quantum causal structures
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Information recoverability of noisy quantum states
• Quantifying the performance of approximate teleportation and quantum error correction via symmetric two-PPT-extendibility
• Sequential generalized measurements: Asymptotics, typicality and emergent projective measurements
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• Relating non-local quantum computation to information theoretic cryptography
• General Continuity Bounds for Quantum Relative Entropies
• Composition rules for quantum processes: a no-go theorem
• The Entropy Power Inequality with quantum conditioning
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Qsun: an open-source platform towards practical quantum machine learning applications
• Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
• Structure-preserving numerical schemes for Lindblad equations
• Procrustean entanglement concentration in quantum-classical networking
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Modeling and simulation of a quantum thermal noise on the qubit
• Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach
• Minimal control power of controlled dense coding and genuine tripartite entanglement
• The wave operator representation of quantum and classical dynamics
• Entropy of the BEC Ground State: Correlation vs Ground State Entropy
• Geometric-Like imaginarity: quantification and state conversion
• Operational meanings of a generalized conditional expectation in quantum metrology
• Degradability of Fermionic Gaussian Channels
• Recoverability for Holevo's just-as-good fidelity
• Non-additivity in classical-quantum wiretap channels
• Fundamental quantum limits in optical metrology from rate-distortion theory
• Quantum State-Channel Duality for the calculation of Standard Model scattering amplitudes
• The Mpemba effect in quantum oscillating and two-level systems
• Measuring non-Markovianity via incoherent mixing with Markovian dynamics
• On entropic uncertainty relations for measurements of energy and its "complement"
• Theory of versatile fidelity estimation with confidence
• Optimality Condition for the Petz Map
• Quantum algorithms for matrix geometric means
• Coherent Quantum Channel Discrimination
• Quantum Operations on Conformal Nets
• Geometric decoherence in diffusive open quantum systems
• The noisy Werner-Holevo channel and its properties
• Capturing long-range memory structures with tree-geometry process tensors
• Quantum resource theory of coding for error correction
• Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
• Quantum Capacity of Partially Corrupted Quantum Network
• Complexity in algebraic QFT
• Logarithmic-Depth Quantum Circuits for Hamming Weight Projections
• Inevitability of knowing less than nothing
• One-shot quantum state exchange
• Partial Transpose Moments, Principal Minors and Entanglement Detection
• On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations
• Entropic No-Disturbance as a Physical Principle
• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
• Efficient Computation of the Quantum Rate-Distortion Function
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Quantum enhancement of randomness distribution
• Generalizing Entanglement
• Upper bounds on the private capacity for bosonic Gaussian channels
• Uncertainty and certainty relations for quantum coherence with respect to design-structured POVMs
• Weyl channels for multipartite systems
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• Quantum channels that destroy negative conditional entropy
• Information transmission with continuous variable quantum erasure channels
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• Capacity of a lossy photon channel with direct detection
• Entangling non planar molecules via inversion doublet transition with negligible spontaneous emission
• Entanglement cost for infinite-dimensional physical systems
• Single-particle steering and nonlocality: The consecutive Stern-Gerlach Experiments
• Transition probabilities and transition rates in discrete phase space
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Low-cost limit of classical communication with restricted quantum measurements
• Connecting XOR and XOR* games
• On the minimum output entropy of random orthogonal quantum channels
• Asymptotic quantification of entanglement with a single copy
• Quantum cryptographic resource distillation and entanglement
• Towards Optimal Quantum Ranging -- Hypothesis Testing for an Unknown Return Signal
• Quantum information criteria for model selection in quantum state estimation
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Random covariant quantum channels
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Neutrino flavor-mass uncertainty relations and an entanglement-assisted determination of the PMNS matrix
• Computing the quantum guesswork: a quadratic assignment problem
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Rate Reduction of Blind Quantum Data Compression with Local Approximations Based on Unstable Structure of Quantum States
• Blindly Factorizing 21 Quantumly
• Kelly Betting with Quantum Payoff: a continuous variable approach
• Optimal one-shot entanglement sharing
• Unified Approach to Witness Nonentanglement-Breaking Quantum Channels
• Quantum channels and some absolute properties of quantum states
• Adversarial guesswork with quantum side information
• Postselected communication over quantum channels
• Information-theoretic aspects of the generalized amplitude damping channel
• Spin-bounded correlations: rotation boxes within and beyond quantum theory
• Time-Efficient Quantum Entropy Estimator via Samplizer
• Quantum channels, complex Stiefel manifolds, and optimization
• Rényi-Holevo inequality from $\alpha$-$z$-Rényi relative entropies
• Single-shot work extraction in quantum thermodynamics revisited
• Unambiguous discrimination of general quantum operations
• Information theoretic parameters of non-commutative graphs and convex corners
• Bounding the quantum capacity with flagged extensions
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Perspectives on Utilization of Measurements in Quantum Algorithms
• Observability of a Sharp Majorana Transition in a Few-Body Model
• Entropy Production from Maximum Entropy Principle: a Unifying Approach
• A direct interferometric test of the nonlinear phase shift gate
• Entanglement entropy evolution during gravitational collapse
• Extending Resource Monotones using Kan Extensions
• Bounding and Estimating the Classical Information Rate of Quantum Channels with Memory
• Directional scrambling of quantum information in helical multiferroics
• Fröhlich-coupled qubits interacting with fermionic baths
• Tradeoff relations between accessible information, informational power, and purity
• Bounding conditional entropy of bipartite states with Bell operators
• Perturbative criteria for the ergodicity of interacting dissipative quantum lattice systems
• Observable-enriched entanglement
• Characterization of non-adaptive Clifford channels
• Distillation of maximally correlated bosonic matter from many-body quantum coherence
• Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System
• When Recall Fails, Discord Remembers: A Quantum Analogue of Kuhn's Theorem
• Classical State Masking over a Quantum Channel
• Compression of quantum shallow-circuit states
• Capacity of Summation over a Symmetric Quantum Erasure MAC with Partially Replicated Inputs
• One-shot and asymptotic classical capacity in general physical theories
• Realizing quantum advantage without entanglement in single-photon states
• An additive refinement of quantum channel capacities
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm
• Quantum detailed balance via elementary transitions