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In order to predict the future state of a quantum system, we generally do not need to know the past state of the entire universe, but only the state of a finite neighborhood of the system. This locality is best expressed as a restriction on how information "flows" between systems. In this talk I will describe some recent work, inspired by quantum cellular automata, about the information strucutre of local quantum dynamics. Issues to be discussed include the definition of "locality", some characterization theorems, connections between classical and quantum locality for reversible maps, the relation between local and global dynamics, and the dissection of CNOT.

In this talk, I will outline a quantum generalization of causal networks that are used to analyze complex probabilistic inference problems involving large numbers of correlated random variables. I will review the framework of classical causal networks and the graph theoretical constructions that are abstracted from them, including entailed conditional independence, d-separation and Markov equivalence. I will show how to generalize the definition of causal networks to the quantum case, such that the same graph theoretic constructions apply, and give an explicit representation of the states supported on the graph as the Gibbs states of certain classes of Hamiltonians.