One Hundred Years After Heisenberg: Discovering the World of Simultaneous Measurements of Noncommuting Observables
One hundred years after Heisenberg’s Uncertainty Principle, the question of how to make simultaneous measurements of noncommuting observables lingers. I will survey one hundred years of measurement theory, which brings us to the point where we can formulate how to measure any set observables weakly and simultaneously and then concatenate such measurements continuously to determine what is a strong measurement of the same observables. The description of the measurements is independent of quantum states---this we call instrument autonomy---and even independent of Hilbert space---this we call the universal Instrument Manifold Program. But what space, if not Hilbert space? It’s a whole new world: the Kraus operators of an instrument live in a Lie-group manifold generated by the measured observables themselves. I will describe measuring position and momentum and measuring the three components of angular momentum, special cases where the instrument approaches asymptotically a phase-space boundary of the instrumental Lie-group manifold populated by coherent states; these special universal instruments are pre-quantum in the sense that they structure any Hilbert space in which they are represented. In contrast, for almost all sets of observables other than these special cases, the universal instrument descends into chaos ... literally.
This work was done with Christopher S. Jackson, whose genius and vision inform every aspect.