Talks

For many optimal measurement problems of interest, the problem may be re-cast as a semi-definite program, for which efficient numerical techniques are available. Nevertheless, numerical solutions give limited insight into more general instances of the problem, and further, analytical solutions may be desirable when an optimised measurement appears as a sub-problem in a larger problem of interest. I will discuss analytical techniques for finding optimal measurements for state discrimination with minimum error and present applications to studying the gap between the theoretically optimal measurement and simpler, experimentally achievable schemes for bi-partite measurement problems.

Quantized lattices, or q-lattices, appear naturally through categorification constructions (for example from zigzag-algebras), but they haven't been studied from a lattice theory point of view. After establishing the necessary background, we'll explain the q-versions of various lattice theory concepts illustrated with examples from combinatorics and graph theory, and we'll list a number of open problems.