High-Temperature Gibbs States are Unentangled and Efficiently Preparable

Understand

We show that thermal states of local Hamiltonians are separable above a constant temperature.

• Specifically, for a local Hamiltonian $H$ on a graph with degree $\mathfrak{d}$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho = e^{-\beta H}/ \operatorname{tr}(e^{-\beta H})$, is a classical distribution over product states for all $\beta < 1/(c\mathfrak{d})$, where $c$ is a constant.
• This proof of sudden death of thermal entanglement resolves the fundamental question of whether many-body systems can exhibit entanglement at high temperature.
• Moreover, we show that we can efficiently sample from the distribution over product states.