In 2004, Horodecki et al., showed that the amount of secret key that can be extracted from noisy bipartite quantum states may exceed the amount of distillable maximally entangled quantum bits. Their work was based on the intuition of quantum data hiding, but did not offer a quantitative relationship to this phenomenon.In this work, which is set in a one-way classical communication scenario, we define a rate of quantum data hiding and provide entropic bounds on it. We then relate the quantum data hiding rate to the gap between the rates at which secret key and entanglement can be extracted, improving on earlier work on this topic.