Title:
A Century after Heisenberg: Discovering the World of Simultaneous Measurements of Noncommuting Observables.
Abstract:
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 simultaneous measurement of the same observables. The description of the measurements is independent of quantum states—we call this instrument autonomy—and even independent of Hilbert space—we call this the universal instrument program. But what space, if not Hilbert space? It’s a whole new world: the Kraus operators of a universal instrument live in a universal 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 group manifold populated by coherent states; these special primitive instruments 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 informs every aspect.
About the speaker:
Carlton M. Caves is a theoretical physicist who has worked mainly on quantum metrology, the science of how to make the most sensitive measurements in the presence of the inherent uncertainties introduced by quantum mechanics. Caves was an undergraduate at Rice University, from which he received a BA in Physics and Mathematics in 1972. He received the PhD in Physics from the California Institute of Technology in 1979 and continued at Caltech as a Research Fellow and then Senior Research Fellow till 1987. From 1988 till 1992 he was Associate Professor of Electrical Engineering and Physics at the University of Southern California. He moved to the University of New Mexico as Professor of Physics and Astronomy in 1992, was recognized as a Distinguished Professor in 2006, and was Director of UNM’s Center for Quantum Information and Control from its founding in 2009 till his retirement from teaching and administration in 2018. Now Distinguished Professor Emeritus at UNM, Caves is a Fellow of the American Physical Society and the American Association for the Advancement of Science and a member of the US National Academy of Sciences.
This lecture is part of the program "Introduction to Precision Measurements and Quantum Metrology"