Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

Understand

We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e.

• we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible.
• We consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels.
• In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity.