How is Amazon using Deep Learning in the new Amazon Go?
" Our Just Walk Out technology automatically detects when products are taken from or returned to the shelves and keeps track of them in a virtual cart. "

Out of this sentence I understand that camera's will record everything you do. Based on these videos they will record the things you bought etc. To get the information out the video deep learning will be used. 

A quick search on google about "video analysis deep neural network" will give you results like: https://arxiv.org/abs/1512.03131