Howie Jordan (Department of Mathematics, CU Boulder)
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Information theory can be said to derive from a logic of partitions or distinctions, in a manner dual to the derivation of classical probability from the more familiar logic of subsets. Then, just as we "linearize" classical subsets and probability to linear subspaces and quantum probabilities, we may linearize partition logic to obtain a logic of direct sum decompositions. We will outline the dual relationship between subsets and partitions from the perspective of categorical logic and use it to motivate a formulation of the corresponding linearized (quantum) logics. In particular, we connect this approach to the program of axiomatizing the category of complete inner product (Hilbert) spaces, which recently found its successful conclusion.
The seminar will be held in hybrid mode. Join Zoom Meeting https://cuboulder.zoom.us/j/94002553301 Passcode 790356
Categorical Partition Logic for (Quantum) Information