A Survey on Quantum Channel Capacities

Abstract

Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.

58 pages, Journal-ref: IEEE Communications Surveys and Tutorials (2018) (updated & improved version of arXiv:1208.1270)

References in corpus (202)

• Quantum entanglement
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• The Quantum Internet
• Mixed State Entanglement and Quantum Error Correction
• Quantum cryptography: Public key distribution and coin tossing
• Long-distance quantum communication with atomic ensembles and linear optics
• Concentrating Partial Entanglement by Local Operations
• Good Quantum Error-Correcting Codes Exist
• Satellite-to-ground quantum key distribution
• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Computing with Very Noisy Devices
• The Role of Relative Entropy in Quantum Information Theory
• Quantum Nonlocality without Entanglement
• Conditions for a class of entanglement transformations
• Reliable Quantum Computers
• State preservation by repetitive error detection in a superconducting quantum circuit
• Distillation of secret key and entanglement from quantum states
• Experimental demonstration of long-distance continuous-variable quantum key distribution
• Remote State Preparation
• Quantum Error Correction and Orthogonal Geometry
• Quantum repeaters based on entanglement purification
• The capacity of the noisy quantum channel
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Quantum teleportation using active feed-forward between two Canary Islands
• Quantum Secure Direct Communication with Quantum Memory
• Quantum data processing and error correction
• Noncommuting mixed states cannot be broadcast
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• General Entanglement Breaking Channels
• Superadditivity of communication capacity using entangled inputs
• Maintaining coherence in Quantum Computers
• Provably Secure and Practical Quantum Key Distribution over 307 km of Optical Fibre
• From quantum cellular automata to quantum lattice gases
• Quantum information can be negative
• Coding Theorem and Strong Converse for Quantum Channels
• Experimental demonstration of a BDCZ quantum repeater node
• Negative entropy and information in quantum mechanics
• The Bloch Vector for N-Level Systems
• Quantum random number generation
• Information transmission through a noisy quantum channel
• Quantum-assisted and Quantum-based Solutions in Wireless Systems
• Codes for the Quantum Erasure Channel
• Capacities of Quantum Erasure Channels
• Quantum Communication With Zero-Capacity Channels
• A quantum information processor with trapped ions
• Entanglement purification and quantum error correction
• Generation of heralded entanglement between distant hole spins
• Quantum Repeater with Encoding
• Dephasing of a superconducting qubit induced by photon noise
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• Quantum Channel Capacity of Very Noisy Channels
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Quantum state merging and negative information
• What is the Computational Value of Finite Range Tunneling?
• Quantum Reverse Shannon Theorem
• From quantum fusiliers to high-performance networks
• High-fidelity transmission of entanglement over a high-loss freespace channel
• On the von Neumann capacity of noisy quantum channels
• A Resource Framework for Quantum Shannon Theory
• Universal enhancement of the optical readout fidelity of single electron spins
• Additivity for a class of unital qubit channels
• On Quantum Fidelities and Channel Capacities
• Path Selection for Quantum Repeater Networks
• Quantum Capacities of Bosonic Channels
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• A Deterministic and Storable Single-Photon Source Based on Quantum Memory
• Asymmetric quantum error correcting codes
• A decoupling approach to the quantum capacity
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• System Design for a Long-Line Quantum Repeater
• Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light
• Fault tolerant quantum computation with very high threshold for loss errors
• Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction
• Basics of Quantum Computation
• Coherence of qubits based on single Ca${}^{+}$ ions
• Improving zero-error classical communication with entanglement
• Information-capacity description of spin-chain correlations
• Degenerate Quantum Codes for Pauli Channels
• Quantum network communication -- the butterfly and beyond
• Prior entanglement between senders enables perfect quantum network coding with modification
• Remote preparation of quantum states
• Quantum complex networks
• Coherence of Spin Qubits in Silicon
• A family of quantum protocols
• Entanglement-Assisted Capacity of Quantum Multiple-Access Channels
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Quantum receiver beyond the standard quantum limit of coherent optical communication
• Initializing, manipulating and storing quantum information with bismuth dopants in silicon
• Classical data compression with quantum side information
• Information Tradeoff Relations for Finite-Strength Quantum Measurements
• The structure of degradable quantum channels
• Quantum broadcast channels
• Google in a Quantum Network
• Information-theoretic approach to quantum error correction and reversible measurement
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• Coherent Communication of Classical Messages
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Experimental quantum key distribution without monitoring signal disturbance
• On entanglement-assisted classical capacity
• Quantum Repeaters using Coherent-State Communication
• Reverse Coherent Information
• Entanglement-assisted quantum turbo codes
• Secret sharing of a quantum state
• Quantum privacy and quantum coherence
• Universal Quantum Information Compression
• Surface code with decoherence: An analysis of three superconducting architectures
• The Capacity of the Quantum Multiple Access Channel
• Quantum Capacities of Channels with small Environment
• The classical communication cost of entanglement manipulation: Is entanglement an inter-convertible resource?
• The private capacity of quantum channels is not additive
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• The quantum capacity with symmetric side channels
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Continuity of quantum channel capacities
• Rate analysis for a hybrid quantum repeater
• Adaptive Real Time Selection for Quantum Key Distribution in Lossy and Turbulent Free-Space Channels
• A General Fidelity Limit for Quantum Channels
• Trade-off capacities of the quantum Hadamard channels
• A high bandwidth quantum repeater
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Perfect Quantum Network Communication Protocol Based on Classical Network Coding
• A father protocol for quantum broadcast channels
• Quantum network coding for quantum repeaters
• On the communication cost of entanglement transformations
• "Extrinsic" and "intrinsic" data in quantum measurements: asymptotic convex decomposition of positive operator valued measures
• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate
• Typical entanglement of stabilizer states
• Teleportation-based realization of an optical quantum two-qubit entangling gate
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• Limits for compression of quantum information carried by ensembles of mixed states
• Additive Asymmetric Quantum Codes
• Hastings' additivity counterexample via Dvoretzky's theorem
• Generalized relative entropies and the capacity of classical-quantum channels
• Quantum simulators, continuous-time automata, and translationally invariant systems
• Extensive nonadditivity of privacy
• Comments on Hastings' Additivity Counterexamples
• Quantum entanglement and classical communication through a depolarising channel
• Communication Links for Distributed Quantum Computation
• Deterministic optical quantum computer using photonic modules
• CSS-like Constructions of Asymmetric Quantum Codes
• Private information via the Unruh effect
• EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
• Entanglement Swapping of Two Arbitrarily Degraded Entangled States
• Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel
• The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels
• Loss in hybrid qubit-bus couplings and gates
• A simple family of nonadditive quantum codes
• Analysis of Quantum Network Coding for Realistic Repeater Networks
• Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel
• Quantum Feedback Channels
• The quantum dynamic capacity formula of a quantum channel
• Noisy Preprocessing and the Distillation of Private States
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Universal quantum data compression via gentle tomography
• Engineering correlation and entanglement dynamics in spin systems
• Gaussianization and eigenvalue statistics for random quantum channels (III)
• The Holevo capacity of infinite dimensional channels and the additivity problem
• On quantum coding for ensembles of mixed states
• Classical information capacity of a class of quantum channels
• Additive Extensions of a Quantum Channel
• Indeterminate-length quantum coding
• Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results
• When does noise increase the quantum capacity?
• An Infinite Sequence of Additive Channels: the Classical Capacity of Cloning Channels
• Entanglement can increase asymptotic rates of zero-error classical communication over classical channels
• Compression of quantum measurement operations
• The quantum capacity is properly defined without encodings
• Public and private resource trade-offs for a quantum channel
• Ergodicity of quantum cellular automata
• Nonadditivity effects in classical capacities of quantum multiple-access channels
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Optimal superdense coding of entangled states
• Remote preparation of three-photon entangled states via single-photon measurement
• Optimal entanglement generation for efficient hybrid quantum repeaters
• Maximal output purity and capacity for asymmetric unital qudit channels
• Entanglement of random subspaces via the Hastings bound
• From f-divergence to quantum quasi-entropies and their use
• Coherent Communication with Continuous Quantum Variables
• Capacity of Quantum Channels Using Product Measurements
• Random quantum codes from Gaussian ensembles and an uncertainty relation
• Qubit Channels Can Require More Than Two Inputs to Achieve Capacity
• The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension
• For quantum information, two wrongs can make a right
• On the classical capacity of quantum Gaussian channels
• Quantum Coding Theorem for Mixed States
• Quantum Networks for Concentrating Entanglement
• Can non-private channels transmit quantum information?
• Correction of beam wander for a free-space quantum key distribution system operating in urban environment
• The Structure and Quantum Capacity of a Partially Degradable Quantum Channel
• Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels
• Quantum Information Transmission over a Partially Degradable Channel
• Capacity Theorems for Quantum Multiple Access Channels
• The Private Classical Capacity of a Partially Degradable Quantum Channel
• Phase control of a longitudinal momentum entangled photon state by a deformable membrane mirror
• Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels
• Quasi-Superactivation of Classical Capacity of Zero-Capacity Quantum Channels
• Public Quantum Communication and Superactivation
• Complementarity and the algebraic structure of 4-level quantum systems

Cited by in corpus (90)

• Continuous-Variable Quantum Key Distribution with Gaussian Modulation -- The Theory of Practical Implementations
• Quantum Low-Density Parity-Check Codes
• When Entanglement meets Classical Communications: Quantum Teleportation for the Quantum Internet (Invited Paper)
• Towards a Distributed Quantum Computing Ecosystem
• Quantum-secured blockchain
• Quantum Internet Protocol Stack: a Comprehensive Survey
• The Evolution of Quantum Secure Direct Communication: On the Road to the Qinternet
• Heralded Generation and Detection of Entangled Microwave--Optical Photon Pairs
• Decentralized Base-Graph Routing for the Quantum Internet
• Satellite-based Quantum Information Networks: Use cases, Architecture, and Roadmap
• Opportunistic Entanglement Distribution for the Quantum Internet
• Semidefinite programming relaxations for quantum correlations
• Training Optimization for Gate-Model Quantum Neural Networks
• Entanglement Availability Differentiation Service for the Quantum Internet
• Entanglement Access Control for the Quantum Internet
• Optimizing High-Efficiency Quantum Memory with Quantum Machine Learning for Near-Term Quantum Devices
• Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
• Quantum capacity analysis of multi-level amplitude damping channels
• Hybrid Quantum Investment Optimization with Minimal Holding Period
• Multilayer Optimization for the Quantum Internet
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Roadmap on Quantum Thermodynamics
• Beyond Shannon Limits: Quantum Communications through Quantum Paths
• Entanglement Accessibility Measures for the Quantum Internet
• Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers
• Probing quantum features of photosynthetic organisms
• Dense Quantum Measurement Theory
• Adaptive Routing for Quantum Memory Failures in the Quantum Internet
• Relative entropies of quantum channels with applications in resource theory
• Quantum Circuit Design for Objective Function Maximization in Gate-Model Quantum Computers
• Traversable Wormholes as Quantum Channels: Exploring CFT Entanglement Structure and Channel Capacity in Holography
• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• Topology Adaption for the Quantum Internet
• Entanglement Verification in Quantum Networks with Tampered Nodes
• Classical capacity of the generalized Pauli channels
• Short Codes for Quantum Channels with One Prevalent Pauli Error Type
• Surpassing the Classical Limit in Magic Square Game with Distant Quantum Dots Coupled to Optical Cavities
• Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters
• Witnessing Negative Conditional Entropy
• Relativistic quantum communication between harmonic oscillator detectors
• Quantum Work Capacitances: ultimate limits for energy extraction on noisy quantum batteries
• Speed-up Quantum Perceptron via Shortcuts to Adiabaticity
• Networked Quantum Services
• Accurate optimal quantum error correction thresholds from coherent information
• Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Theory of Noise-Scaled Stability Bounds and Entanglement Rate Maximization in the Quantum Internet
• Resonant Multilevel Amplitude Damping Channels
• State Stabilization for Gate-Model Quantum Computers
• Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Partially Coherent Direct Sum Channels
• Experimental observation of coherent-information superadditivity in a dephrasure channel
• Quantum outage probability for time-varying quantum channels
• Capacities of the covariant Pauli channel
• Classical communication through quantum causal structures
• Systematic Design and Optimization of Quantum Circuits for Stabilizer Codes
• Positive Maps From Irreducibly Covariant Operators
• Mitigating errors in logical qubits
• Entanglement catalysis for quantum states and noisy channels
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Theory of Quantum Gravity Information Processing
• Transmission of quantum information through quantum fields in curved spacetimes
• An agnostic-Dolinar receiver for coherent states classification
• Information flow and error scaling for fully-quantum control
• Naimark extension for the single-photon canonical phase measurement
• A Poisson Model for Entanglement Optimization in the Quantum Internet
• Quantum channels that destroy negative conditional entropy
• Weyl channels for multipartite systems
• Information transmission with continuous variable quantum erasure channels
• Profitable entanglement for channel discrimination
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Quantum Inception Score
• Nonlinear protocol for high-dimensional quantum teleportation
• Quantum channels and some absolute properties of quantum states
• Quantum JPEG
• A complete continuous-variable quantum computation architecture based on the 2D spatiotemporal cluster state
• The simulation of distributed quantum algorithms
• Approaching optimal microwave-acoustic transduction on lithium niobate using SQUID arrays
• Dephasing effects on quantum correlations and teleportation in presence of state dependent bath
• Multi-mode CV-QKD with Noiseless Attenuation and Amplification
• Improving classical capacity of qubit dynamical maps through stationary state manipulation
• Optimizing quantum codes with an application to the loss channel with partial erasure information
• On Simultaneous Information and Energy Transmission through Quantum Channels
• No-go theorem for environment-assisted invariance in non-unitary dynamics
• Channel induced dynamics of quantum information in mixed state free QFTs
• Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps
• Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection
• Simulation of entanglement based quantum networks for performance characterization
• Adiabatic Dynamics of Entanglement