If you will go through this article, it is clearly written :
When deploying to non-production environments (sandbox), Apex tests aren’t required and aren’t run automatically. When using Metadata API (including the Force.com Migration Tool), Quick Deploy is supported in sandbox only for validations that explicitly enable the execution of tests (for example, via the runAllTests parameter for the Migration Tool). For change sets, Quick Deploy is not supported in sandbox because there is no option to enable test runs for change sets.
So it seems like, using Metadata API(ANT), it is supported only in sandbox(with runAllTests paramater enabled)