Here are a couple of articles recently published by Nature. They are contradictory to some degree- one says there seems to be many more infected as compared to official numbers, the other articles indicates the tests aren't really reliable. These articles are aggregates of other information.
This mentions some issues raised earlier in the thread regarding how good the antibody tests might be.
"It seems that many tests available now are not accurate enough at identifying people who have had the disease, a property called test sensitivity, and those who haven’t been infected, known as test specificity. A high-quality test should achieve 99% or more sensitivity and specificity, adds Collignon. That means that testing should turn up only about 1 false positive and 1 false negative for every 100 true positive and true negative results.