We first summarize background on the quantum capacity of a quantum channel, and explain why we know very little about this fundamental quantity, even for the qubit depolarizing channel (the quantum analogue of the binary symmetric channel) despite 20 years of effort by the community.
Then, we focus on low-noise quantum channels, and present recent results on the quantum capacity to leading order in the noise parameter. This in particular solves the quantum capacity problem (to leading order) for the qubit depolarizing channel, and provides a structure theorem for the capacity achieving codes. For low-noise channels, degenerate codes provide negligible superadditivity effect.
Analoguous results on the private capacity will be presented. Our results imply that for low-noise channels, there is negligible difference between coherence and privacy, and a key rate approaching the capacity can already be obtained using classical error correction and privacy amplification.
Joint work with Felix Leditzky and Graeme Smith
- Quantum Information
- Scientific Series