Actually, from the article, it mentions this:

> Leanne Kemp, an Australian who in 2015 founded a company called Everledger, has now encrypted the distinguishing features of 1.8 million diamonds and their provenance on a blockchain.

> More than 40 features are logged to create a fingerprint for each diamond, logging it from mine to ring.

So it seems, in the case of diamonds, they are unique enough to create a fingerprint. I'm no expert on diamonds, so that might not really work in reality.