The research is more centered around a specific use of Kolmogorov's classical probability theory, which takes context into consideration. This realization has a

The research is more centered around a specific use of Kolmogorov's classical probability theory, which takes context into consideration. This realization has allowed "classical probability theory" to be used in a characteristically "quantum" way, by paying attention to higher dimensional probability distributions, and how "observation" tends to draw these probability distributions through lower dimensional subspaces. Some people doing this research also employ fancier probability theories, but to me it is profound that classical probability theory can be used in the same basic way. So yeah, the research relies on linear algebra, sure, but specifically in the same way quantum theory relies on linear algebra: as a way of projecting probability distributions into different subspaces during measurement ("collapsing the wavefunction").