Characterizing ground and thermal states of few-body Hamiltonians

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.

9 pages, 5 figures, v2: final version

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• Almost all four-particle pure states are determined by their two-body marginals
• Entanglement transitivity problems
• Uniquely determined pure quantum states need not be unique ground states of quasi-local Hamiltonians
• Quantum LOSR networks cannot generate graph states with high fidelity
• On the complexity of finding the maximum entropy compatible quantum state
• Multipartite States under Elementary Local Operations
• The additivity of states uniquely determined by marginals
• Investigating Pure State Uniqueness in Tomography via Optimization
• Analysing multiparticle quantum states
• Matrix systems, algebras, and open maps