Multipartite entanglement and few-body Hamiltonians

TL;DR

This paper explores how to engineer Hamiltonians with short-range, few-body interactions to produce highly multipartite-entangled states, like MMES and GHZ states, as nondegenerate eigenstates in small quantum systems.

Contribution

It identifies conditions and bounds for constructing Hamiltonians that have maximally multipartite-entangled states as unique eigenstates in small qubit systems.

Findings

Conditions for Hamiltonians with MMES as eigenstates

Bounds on the number of qubits for GHZ eigenstates

Insights into applications of such Hamiltonians

Abstract

We investigate the possibility to obtain higly multipartite-entangled states as nondegenerate eigenstates of Hamiltonians that involve only short-range and few-body interactions. We study small-size systems (with a number of qubits ranging from three to five) and search for Hamiltonians with a Maximally Multipartite Entangled State (MMES) as a nondegenerate eigenstate. We then find conditions, including bounds on the number of coupled qubits, to build a Hamiltonian with a Greenberger-Horne-Zeilinger (GHZ) state as a nondegenerate eigenstate. We finally comment on possible applications.