Speaker
Description
In this talk I discuss the problem posed by Magan of deriving sharp entropic uncertainty relations from the entropic certainty principle. I introduce a quadratic form measuring the failure of observables to commute with the momentum subalgebra. This gives rise to a flow whose trajectories are operator-valued paths. I show that relative entropy along the induced flow of states converges to the relative entropy of their restrictions to the fixed-point algebra of the flow. An explicit entropy-production formula then expresses the resulting loss of relative entropy as an improper integral. I discuss an AI-assisted analytic computation proving Gaussian vector states saturate the expected lower bound in the continuum limit. I conclude by outlining an argument, still under verification, that would establish this lower bound for all normalized Schwartz wavefunctions and thereby yield the sharp entropic uncertainty inequality of Beckner–Białynicki-Birula–Mycielski.