High-Temperature Gibbs States are Unentangled and Efficiently Preparable
Host
Rahul Ilango
MIT
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 $d$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho =e^{-\beta H}/ \tr(e^{-\beta H})$, is a classical distribution over product states for all $\beta < 1/(c d)$, 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. In particular, for any $\beta < 1/( c d^2)$, we can prepare a state $\eps$-close to $\rho$ in trace distance with a depth-one quantum circuit and $\poly(n, 1/\eps)$ classical overhead.
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 $d$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho =e^{-\beta H}/ \tr(e^{-\beta H})$, is a classical distribution over product states for all $\beta < 1/(c d)$, 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. In particular, for any $\beta < 1/( c d^2)$, we can prepare a state $\eps$-close to $\rho$ in trace distance with a depth-one quantum circuit and $\poly(n, 1/\eps)$ classical overhead.