In his article/lecture on "What quantum physics can learn from Egyptian hieroglyphs"", researcher Robert Spekkens talks about Clifford fragments. He describes them as "containing only a subset of the full set of quantum states and measurements – which admit of an interpretation where every quantum state can be understood as a mathematical encoding of a probability distribution over a set of deeper physical states."
What are Clifford fragments, and is there any literature available on them? Particularly, are they connected to Clifford Algebra? A fast google search of the term "Clifford fragments" returns only what appear to be disconnected results.