I use a no dig technique for my potatoes, using landcape fabric instead of plastic sheeting. I alway make sure they are well chitted before planting. I then plant through precut slits in the fabric, to roughly the depth of the trowel. I find this is the best depth, any deeper and the tubers use too much energy reaching the surface. Even so it takes a while before the shoots emerge. I could add a mulch on top of the fabric, but this isnt really nesesary, (and i dont normaly have anything spare to use).
When it comes to harvesting I just have to pull back the fabric and scrape around carefully with a trowel. Ok some digging involved here as the tubers can be quite deep, but not so much as with the traditional method.