Mary Beth Ruskai: Some old and new results on quantum marginals and reduced density matrices

Mary Beth Ruskai, Tufts University

Abstract

It is well known that the set of m-body reduced density matrices of N-body states (possibly satisfying a symmetry constraint) is convex. This also holds for vectors of m-body quantum marginals.

Recent work in quantum information theory has regenerated interest in the role of reduced density matrices in many-body quantum theory and led to the resolution of some long-standing questions. One of these is the realization that an extreme point can have a non-unique pre-image, and that such situations are related to quantum error correction codes.

This talk will provide a brief survey of old and new work, and describe some of the open questions which remain.