Quantum Inception Score as an Expressivity Measure of the Quantum Generative Models*

We propose the quantum inception score, which quantifies the richness of the expressive power of the quantum generative models. We relate the quantum inception score to the classical capacity of the quantum channel operating as a classifier, which enables us to prove that the quantum generative models can achieve richer expressivity than its classical counterparts due to the presence of the quantum coherence and entanglement. Further, we employ the quantum fluctuation theorem to characterize the expressivity degradation of the quantum generative models due to the quantum decoherence.