Characterizing ground and thermal states of few-body Hamiltonians

TL;DR

This paper develops methods to identify and characterize ground and thermal states of few-body Hamiltonians, providing insights into state complexity, entanglement, and certification for quantum simulations.

Contribution

It introduces new techniques to characterize states generated by k-body Hamiltonians and their convex hulls, advancing understanding of state determination and entanglement.

Findings

Characterization methods for states from two- and k-body Hamiltonians

Insights into state determination by marginals

Certification techniques for quantum simulation

Abstract

The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k-body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived.