Coding Theorems of Quantum Information Theory
arXiv:quant-ph/9907077
Abstract
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information transmission via quantum channels we give a new proof of the coding theorem, and prove the strong converse, even under the extended model of nonstationary channels. As a by-product we obtain a new proof of the famous Holevo bound. Then multi-user systems are investigated, and the capacity region for the quantum multiple access channel is determined. The last chapter contains a preliminary discussion of some models of compression of correlated quantum sources, and a proposal for a program to obtain operational meaning for quantum conditional entropy. An appendix features the introduction of a notation and calculus of entropy in quantum systems.
80 pages, Ph.D. dissertation, Uni Bielefeld
References in corpus (9)
- Quantum data processing and error correction
- Coding Theorem and Strong Converse for Quantum Channels
- Information transmission through a noisy quantum channel
- Strong Converse to the Quantum Channel Coding Theorem
- Universal Quantum Information Compression
- A General Fidelity Limit for Quantum Channels
- Limits for compression of quantum information carried by ensembles of mixed states
- Multi-access channels in quantum information theory
- Quantum Rate-Distortion Coding
Cited by in corpus (44)
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Coding Theorem and Strong Converse for Quantum Channels
- A Resource Framework for Quantum Shannon Theory
- Distilling common randomness from bipartite quantum states
- Entanglement-assisted communication of classical and quantum information
- Quantum universal variable-length source coding
- Applications of coherent classical communication and the Schur transform to quantum information theory
- Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
- Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
- Exponents of quantum fixed-length pure state source coding
- Compression of sources of probability distributions and density operators
- One-shot lossy quantum data compression
- Duality of privacy amplification against quantum adversaries and data compression with quantum side information
- Achieving the Han-Kobayashi inner bound for the quantum interference channel by sequential decoding
- Strong converse theorems using Rényi entropies
- Compression of quantum measurement operations
- On the distributed compression of quantum information
- Towards a geometrical interpretation of quantum information compression
- Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
- On quantum channels
- Strong converse for the classical capacity of the pure-loss bosonic channel
- Classical Capacities of Averaged and Compound Quantum Channels
- Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance
- Public and private communication with a quantum channel and a secret key
- Properties of Noncommutative Renyi and Augustin Information
- General Mixed State Quantum Data Compression with and without Entanglement Assistance
- Quantum Channel Capacities Per Unit Cost
- Entangled games are hard to approximate
- Algorithmic Information Theoretic Issues in Quantum Mechanics
- A constructive commutative quantum Lovasz Local Lemma, and beyond
- An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma
- Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
- One-shot Multiparty State Merging
- From Quantum Source Compression to Quantum Thermodynamics
- Quantum and Classical Message Identification via Quantum Channels
- How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
- "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
- Sphere-Packing Bound for Symmetric Classical-Quantum Channels
- A strong converse for the quantum state merging protocol
- One-Sided Error QMA with Shared EPR Pairs -- A Simpler Proof
- The definition of a random sequence of qubits: from Noncommutative Algorithmic Probability Theory to Quantum Algorithmic Information Theory and back
- An Elementary Proof of Private Random Number Generation from Bell Inequalities
- The strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory
- Classical feedback for quantum channels