Principles of Quantum Communication Theory: A Modern Approach

Abstract

This is a preliminary version of a book in progress on the theory of quantum communication. We adopt an information-theoretic perspective throughout and give a comprehensive account of fundamental results in quantum communication theory from the past decade (and earlier), with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field. In Part I, we cover mathematical preliminaries and provide a detailed study of quantum mechanics from an information-theoretic perspective. We also provide an extensive and thorough review of quantum entropies, and we devote an entire chapter to the study of entanglement measures. Equipped with these essential tools, in Part II we study classical communication (with and without entanglement assistance), entanglement distillation, quantum communication, secret key distillation, and private communication. In Part III, we cover the latest developments in feedback-assisted communication tasks, such as quantum and classical feedback-assisted communication, LOCC-assisted quantum communication, and secret key agreement.

v2: 1240 pages, 60 figures. Comments welcome!

References in corpus (28)

• The Quantum Chernoff Bound
• Quantum information can be negative
• A complete family of separability criteria
• A No-Go Theorem for Gaussian Quantum Error Correction
• Quantum Capacities of Bosonic Channels
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Degenerate Quantum Codes for Pauli Channels
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Unitary designs and codes
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Unbounded number of channel uses are required to see quantum capacity
• Degradability of Bosonic Gaussian channels
• The decoupling approach to quantum information theory
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Distilling entanglement from arbitrary resources
• A simple proof of monogamy of entanglement
• Remarks on the classical capacity of quantum channel
• Closed formula for the relative entropy of entanglement
• Sine distance for quantum states
• Approximate quantum error correction, random codes, and quantum channel capacity
• Realization schemes for quantum instruments in finite dimensions
• Pretty good measures in quantum information theory
• Relative entropies and their use in quantum information theory
• Qubit channels that achieve capacity with two states
• Multiple Quantum Hypothesis Testing Expressions and Classical-Quantum Channel Converse Bounds
• On the condition of conversion of classical probability distribution families into quantum families
• Quantum Fidelities, Their Duals, And Convex Analysis

Cited by in corpus (34)

• Real quantum operations and state transformations
• Entropic bounds on information backflow
• Distinguishing Random and Black Hole Microstates
• Estimating distinguishability measures on quantum computers
• Computable Rényi mutual information: Area laws and correlations
• Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits
• Testing symmetry on quantum computers
• On the design and analysis of near-term quantum network protocols using Markov decision processes
• Equilibration of Multitime Quantum Processes in Finite Time Intervals
• Bounding the forward classical capacity of bipartite quantum channels
• Fidelity-Based Smooth Min-Relative Entropy: Properties and Applications
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Continuity of characteristics of composite quantum systems
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Gaussian Continuous-Variable Isotropic State
• Entanglement and non-locality in quantum protocols with identical particles
• The SWAP Imposter: Bidirectional Quantum Teleportation and its Performance
• Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• A smallest computable entanglement monotone
• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Postselected communication over quantum channels
• The $\alpha \to 1$ Limit of the Sharp Quantum Rényi Divergence
• Dual Instruments and Sequential Products of Observables
• Chain rules for quantum channels
• A Converse for Fault-tolerant Quantum Computation
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
• On quantum states with a finite-dimensional approximation property
• Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size
• Compactness criterion for families of quantum operations in the strong convergence topology and its applications
• A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits