One-Shot Classical Data Compression With Quantum Side Information and the Distillation of Common Randomness or Secret Keys

The task of compressing classical information in the one-shot scenario is studied in the setting where the decompressor additionally has access to some given quantum side information. In this hybrid classical-quantum version of the famous Slepian-Wolf problem, the smooth max entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information. Combining this result with known results on privacy amplification then yields tight bounds on the amount of common randomness and secret key that can be recovered in one shot from hybrid classical-quantum systems using one-way classical communication.