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In this informal talk, I shall give a short introduction to the field of higher-order quantum transformations, including its subfield of indefinite causal order. I shall discuss some of the motivations and important results in the field, current research directions and open problems, as well potential applications in quantum information processing.

I will begin by reviewing the general mathematical concept of representation. I will then show that representation theory is more generally applicable than one might expect, for example in quantum foundations, in quantum gravity and in machine learning. In those contexts, I will first talk about the notion of representation underlying phenomena of emergence in quantum gravity. I will then discuss how quantum reference frames might be viewed as representations. Finally, I will talk about how transformer models, such as GPT-4, construct representations of what they learn and, in that light, what it may take for machines to reach AGI or even consciousness.  

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Zoom link: https://pitp.zoom.us/j/99349397588?pwd=T056VjZXRWZWT28zY3VOZHFDcmQ3QT09

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 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.

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Zoom link https://pitp.zoom.us/j/94135518267?pwd=T2JOL21VaEcrY05KeG1SYTVYdHhxdz09