Privacy issues arise in a number of computational tasks, notably in learning problems. In this context, differentially private mechanisms ensure that the final output does not depend too heavily on any one input or specific training example. The problem of private learning has been extensively studied. In particular, a striking equivalence between local differentially private algorithms and statistical query algorithms has been shown in [Kas+11]. In addition, the statistical query model has been recently extended to quantum computation in [AGY20]. In this work, we give a formal definition of quantum local differential privacy and we extend the aforementioned result of [Kas+11], addressing an open problem posed in [AQS21].