Theory Seminar: Do Locality Principles Survive Long-Range Interactions? Ground State Stability in Quantum Spin Systems

Kai Schmidt-Brauns
Universität Tübingen
OQS Seminar, at the Seminar Room
Thursday, July 16, 11:30 CET

Quantum Spin Systems (QSS) with long-range interactions provide a natural framework for modelling experimentally relevant quantum platforms (e.g. trapped ions). In quantum information processing, it is essential to control error propagation and the stability of measurement tasks, which are both related to the concept of a computational task's well-posedness. Known stability results primarily address Gibbs states or short-range systems, in which stability can be derived from a deeper locality principle. This principle relates three distinct notions of locality, namely Local Perturbations Perturb Locally, Local Indistinguishability, and Decay of Correlations. In contrast, these locality relations and their implications for stability remain poorly understood for ground states of long-range systems.
In this talk, I will introduce these foundational notions and the established techniques for short-range stability. I will then present to what extent these locality relations may be extended to the long-range, ground state regime, including partial implications and a refined stability result.