> So, a female diploid drone.

I would say, no -- that's not it. As we know, drones normally develop from unfertilized eggs, which are haploid due to the way they are formed. They get only one set of chromosomes from the Mom. However, before the chromosomes are segregated, there is crossing over and recombination, so the drones are not identical twins. 

Normally, the HB eggs are fertilized by a haploid sperm, producing a diploid offspring  (two sets of chromosomes). The mother and father are usually unrelated so a normal female is produced. If the parents are closely related, there may be a close match on the sex loci, producing what it called a diploid drone. For a female to be produced, there have to be different alleles on the sex loci. 

What we have here is thelytoky, where females are produced from unfertilized eggs. They still have to have two sets of chromosomes and they have to be different, or else a diploid drone would develop. Diploid drones are removed by the worker bees, as they apparently regard them as abnormal. The authors state:

> Meiosis proceeds as normal to produce four haploid pronuclei. Two of the four pro-nuclei fuse, as if one acted as a sperm, thereby restoring diploidy and producing a female offspring that is essentially a clone of her mother.  ... thelytoky can occur in queens or workers and has profound consequences for the kin structure of insect societies. ... worker thelytoky means that unmated laying workers can be genetically reincarnated as the next queen ... Thelytoky is rare in most subspecies, but common among queenless workers of A. m. capensis of the Cape provinces of South Africa
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