I am trying to self study aspects of AdS-CFT, particularly the implication of the Ryu-Takayanagi entanglement entropy formula. I have been thinking about the following question and it would be a great help for me if someone could give an answer. In Ads-CFT we can relate different states in the CFT to different geometries in the bulk. For example, the ground state of CFT corresponds to pure AdS, thermal state corresponds to a black hole etc.
But, is there an intuitive way of thinking about mixed states in this context. Given a mixed state in the CFT side what does it correspond to in the bulk? Every mixed state can be written as a sum of pure states weighted with a probability. So, given a mixed state in a CFT, can we decompose it in terms of pure states and say that the AdS dual is not a fixed geometry but rather all the geometries corresponding to the pure states which make up that mixed state?
Due to some reason I feel that the above is a naive way of thinking about the situation as I can't make sense of "all the geometries corresponding to the pure states which make up that mixed state". So, what is a better way of thinking about the same?