Understand
In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998.
- By choosing the optimal input distribution, the bound implies the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate, even in infinite-dimensional Hilbert spaces.
- Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, constant composition codes, and classical data compression with quantum side information via fixed-length or variable-length coding.
- Our technical ingredient is to establish an operator layer cake theorem - the directional derivative of an operator logarithm admits an integral representation of certain projections.