Quantum computation and quantum information
Quantum computation and quantum information
Convex Optimization
Entanglement-assisted communication of classical and quantum information
IEEE Transactions on Information Theory
Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
IEEE Transactions on Information Theory
Optimal trading of classical communication, quantum communication, and entanglement
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
The capacity of the quantum channel with general signal states
IEEE Transactions on Information Theory
On quantum fidelities and channel capacities
IEEE Transactions on Information Theory
Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
IEEE Transactions on Information Theory
The private classical capacity and quantum capacity of a quantum channel
IEEE Transactions on Information Theory
A Resource Framework for Quantum Shannon Theory
IEEE Transactions on Information Theory
An Infinite Sequence of Additive Channels: The Classical Capacity of Cloning Channels
IEEE Transactions on Information Theory
Entanglement-assisted communication of classical and quantum information
IEEE Transactions on Information Theory
Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
IEEE Transactions on Information Theory
Public and private resource trade-offs for a quantum channel
Quantum Information Processing
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The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.