Better transmission with lower capacity: lossy compression over quantum channels

Understand

Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel.

• It, together with the source coding theorem, characterizes lossless channel communication in the classical regime.
• Lossy compression scenarios require the additional description provided by rate-distortion theory, which characterizes the trade-off between compression rate and the distortion of the compressed signal.
• Even in this context, the capacity characterizes the usefulness of a channel -- a channel with more capacity will always outperform a channel with less capacity.