Tema Con Variazioni: Quantum Channel Capacity

Abstract

Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the mathematically precise statements of this idea which have been put forward in the literature. We show that all the variations considered lead to equivalent capacity definitions. In particular, it makes no difference whether one requires mean or maximal errors to go to zero, and it makes no difference whether errors are required to vanish for any sequence of block sizes compatible with the rate, or only for one infinite sequence.

32 pages, uses iopart.cls

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• Quantum Capacities of Channels with small Environment
• Learning the Alpha-bits of Black Holes
• Noise-enhanced classical and quantum capacities in communication networks
• On the power of PPT-preserving and non-signalling codes
• Entanglement Cost of Quantum Channels
• Quantum minimal surfaces from quantum error correction
• Resource theory of asymmetric distinguishability for quantum channels
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Quantum Channel Simulation and the Channel's Smooth Max-Information
• Fundamental limitations on distillation of quantum channel resources
• Energy-constrained private and quantum capacities of quantum channels
• One-shot entanglement-assisted quantum and classical communication
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• Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
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• Approximate quantum error correction, random codes, and quantum channel capacity
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• One-Shot Manipulation of Dynamical Quantum Resources
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• Transmitting qubits through relativistic fields
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• Decoding quantum information via the Petz recovery map
• Channel-Optimized Quantum Error Correction
• Channel Capacities of an Exactly Solvable Spin-Star System
• Quantum to Classical Randomness Extractors
• Approximate simulation of quantum channels
• Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit
• Semidefinite programming hierarchies for constrained bilinear optimization
• Random quantum codes from Gaussian ensembles and an uncertainty relation
• Incomplete quantum process tomography and principle of maximal entropy
• Channel kets, entangled states, and the location of quantum information
• Private states, quantum data hiding and the swapping of perfect secrecy
• Ballistic quantum state transfer in spin chains: general theory for quasi-free models and arbitrary initial states
• Teleportation-Induced Correlated Quantum Channels
• Black holes as bosonic Gaussian channels
• Exact Energy-Time Uncertainty Relation for Arrival Time by Absorption
• Simple test for quantum channel capacity
• Entanglement fidelity of quantum memories
• Fault-tolerant Coding for Quantum Communication
• Quantum Subdivision Capacities and Continuous-time Quantum Coding
• Entanglement fidelity and measurement of entanglement preserving in quantum processes
• Quantum capacity of an amplitude-damping channel with memory
• Quantum channel capacities - multiparty communication
• Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity
• Optimized Entanglement-Assisted Quantum Error Correction
• Entanglement-assisted capacities of compound quantum channels
• Continuity of entropies via integral representations
• Fault-tolerant Coding for Entanglement-Assisted Communication
• Coherent Quantum Channel Discrimination
• Degradable Quantum Channels Using Pure to Product of Pure States Isometries
• On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs
• Computable lower bounds on the entanglement cost of quantum channels
• Quantum enhancement of randomness distribution
• Contravariant Densities, Complete Distances and Relative Fidelities for Quantum Channels
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Shadow Simulation of Quantum Processes
• Random private quantum states
• Adaptive Channel Reshaping for Improved Entanglement Distillation
• Aspects of multistation quantum information broadcasting
• Inequalities for quantum channels assisted by limited resources
• Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture
• Explicit decoders using fixed-point amplitude amplification based on QSVT
• Irreversibility of entanglement loss