High-Temperature Gibbs States are Unentangled and Efficiently Preparable Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang Abstract: 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 ∂, its Gibbs state at inverse temperature β, denoted by ρ = e^(-βH)/tr(e^(-βH)), is a classical distribution over product states for all β < 1/(c∂), 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. In particular, for any β < 1/(c∂²), we can prepare a state ε-close to ρ in trace distance with a depth-one quantum circuit and poly(n, 1/ε) classical overhead. We show that high-temperature Gibbs states are separable and can be efficiently prepared. Our results demonstrate that above a constant temperature, the Gibbs state of any local Hamiltonian exhibits zero entanglement. We also show that high-temperature Gibbs states can be efficiently prepared with a depth-one quantum circuit and poly(n, log(1/ε)) classical overhead. Our results have implications for quantum thermalization and quantum advantage.High-Temperature Gibbs States are Unentangled and Efficiently Preparable Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang Abstract: 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 ∂, its Gibbs state at inverse temperature β, denoted by ρ = e^(-βH)/tr(e^(-βH)), is a classical distribution over product states for all β < 1/(c∂), 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. In particular, for any β < 1/(c∂²), we can prepare a state ε-close to ρ in trace distance with a depth-one quantum circuit and poly(n, 1/ε) classical overhead. We show that high-temperature Gibbs states are separable and can be efficiently prepared. Our results demonstrate that above a constant temperature, the Gibbs state of any local Hamiltonian exhibits zero entanglement. We also show that high-temperature Gibbs states can be efficiently prepared with a depth-one quantum circuit and poly(n, log(1/ε)) classical overhead. Our results have implications for quantum thermalization and quantum advantage.