Talks

The talk concerns a generalization of the concept of a minimum uncertainty state to the finite dimensional case. Instead of considering the product of the variances of two complementary observables we consider an uncertainty relation involving the quadratic Renyi entropies summed over a full set of mutually unbiased bases (MUBs). States which achieve the lower bound set by this inequality were introduced by Wootters and Sussman, who proved existence for every prime power dimension, and by Appleby, Dang and Fuchs who showed that in prime dimension the fiducial vector for a for a symmetric informationally complete positive operator valued measure (SIC-POVM) covariant under the Weyl-Heisenberg group is a state of this kind. Subsequently Sussman proved existence for a class of odd prime power dimensions. The purpose of this talk is to complete the existence proof by showing that minimum uncertainty states exist in every prime power dimension, without exception. Along the way we establish a number of properties of the Clifford group, and Galois extension fields, which might be of some independent interest.

The Great Plague of London, which claimed the lives of one fifth of London\'s population in 1665, is one of the most famous epidemics of all time. We have recently digitized the mortality records for London during the Great Plague, yielding weekly data for each of the 130 parishes. I will describe the temporal and spatial dynamics of the plague, and discuss our efforts to estimate the transmissibility of the infectious agent. I will also briefly describe other projects in progress inspired by disease-specific mortality records for London over the past 650 years.