Tater sprouts?

The oracles say.. only put first class green stuff from toms and pots in your compost hep /composter tub .
These two plants suffer from attacks of blight spores and you are likely to introduce it into your compost .( so check out other close relatives of these two plants.)
The Royal Horticultural Society ( RHS ) website reccommends that you cut the greens off compost if A1 or burn if otherwise .
( some folks send it to the municiple composting and it does not kill the spores .. beware of municiple compost )
Leave the potatoes in the ground undisturbed for a full ten days after removing and disposing of the tops.. this is to stop the spores infecting the lifted potatoes especially those you want to store .

My dad & his farmer boss always said never ever put the tops or spent plants in the compost heap or plough them back into the land because of the chance of infections .

Currently here in the UK the farmers use a mild sulphuric acid micro mist spray to kill off and dessicate the potato tops about 20 days before harvesting them.