Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly. This assumption seems to fail in quantum theory. A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs, in which incompatible experiments are permitted. Among other things, this effort has led to (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement) are in fact generic to nonclassical probabilistic theories, (ii) a suite of reconstructions of (mostly, finitedimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM. This course will offer a survey of this literature, starting from scratch and concluding with a discussion of recent developments.
Mathematical prerequisites: finitedimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).
Scheduling note: There will be 5 lectures from March 1226, then a gap of two weeks before the final 2 lectures held April 16 & 18.
Format: Inperson only; lectures will be recorded for PIRSA but not live on Zoom.
Format results

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University

GPTs and the probabilistic foundations of quantum theory  Lecture
Alexander Wilce Susquehanna University