Quantum Data Compression and Quantum Cross Entropy

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. A central quantity for the theoretical foundation of quantum machine learning is the quantum cross entropy. In this paper, we present one operational interpretation of this quantity, that the quantum cross entropy is the compression rate for sub-optimal quantum source coding. To do so, we give a simple, universal quantum data compression protocol, which is developed based on quantum generalization of variable-length coding, as well as quantum strong typicality.