Repainting Quantum Mechanics on QBist Canvas
Christopher Fuchs
QBism (pronounced cubism) is a foundational program for quantum mechanics premised on the idea that quantum probabilities should be understood as personalist Bayesian probabilities—that is, quantified degrees of belief or gambling attitudes. Philosophers hate it. “Wah, wah, wah, your quantum states aren't real; they have to be real because my philosophy says so!” What the philosophers have never appreciated (or perhaps cared about) is that this turn in thinking has motivated a significant number of theorems in quantum information science that might not have been discovered otherwise. In this talk, I will sketch QBism’s most ambitious project yet—rewriting the quantum formalism so to wear its Bayesian character on its sleeve. One of our key moves will be to replace the notion of Phasenraum (a notion first developed by Paul and Tatyana Ehrenfest, in fact) with the notion of a reference measurement. But which reference measurement is the most revealing of quantum theory’s essence? In trying to answer this question, we will see that it leads to a deep mathematical question related to Hilbert’s still-unsolved 12th problem and suggests a novel measurement (when it exists) with a growing number of applications in quantum information science.