This is a tricky one as it's an effect of marble stone rather than the polish marble effect we're used to seeing.
Assuming you're using a gel polish (any brand will be the same technique for this), I would do one or two coats of base colour to get a solid background then before you cure your last cost of colour, say black, use a very tiny dotting tool or pin to randomly place small dots of white, then drag with a teeny brush to create the fade effect. Might take a bit of trial and error.