The quantum dynamic capacity formula of a quantum channel
arXiv:1004.0458 · doi:10.1007/s11128-011-0310-6
Abstract
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 simplifies the computation of the trade-off surface, 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.
24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimization
References in corpus (3)
Cited by in corpus (24)
- A Survey on Quantum Channel Capacities
- Rate-loss analysis of an efficient quantum repeater architecture
- Approaches for approximate additivity of the Holevo information of quantum channels
- Entanglement-assisted quantum turbo codes
- Entanglement-Based Quantum Information Technology
- Practical route to entanglement-assisted communication over noisy bosonic channels
- Strong converse rates for quantum communication
- Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity
- Quantum trade-off coding for bosonic communication
- Information trade-offs for optical quantum communication
- Potential capacities of quantum channels
- Public and private resource trade-offs for a quantum channel
- Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
- Superadditivity of the Classical Capacity with Limited Entanglement Assistance
- Quantum capacity of bosonic dephasing channel
- Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
- Hadamard quantum broadcast channels
- Capacities of Quantum Amplifier Channels
- Preserving Information from the Beginning to the End of time in a Robertson-Walker Spacetime
- Capacity Estimates via comparison with TRO channels
- Quantum-enabled communication without a phase reference
- New lower bounds to the output entropy of multi-mode quantum Gaussian channels
- Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
- Information storage and transmission under Markovian noise