# High-Temperature Gibbs States are Unentangled and Efficiently Preparable

arXiv: https://arxiv.org/abs/2403.16850 · HTML: https://mlsanity.com/paper/2403.16850/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2024.

## Built on by (most cited first, 6 of 6)

- [Quantum Boltzmann machine learning of ground-state energies](https://mlsanity.com/paper/2410.12935/) (2024)
- [Structure learning of Hamiltonians from real-time evolution](https://mlsanity.com/paper/2405.00082/) (2024)
- [Natural gradient and parameter estimation for quantum Boltzmann machines](https://mlsanity.com/paper/2410.24058/) (2024)
- [Quantum thermodynamics and semi-definite optimization](https://mlsanity.com/paper/2505.04514/) (2025)
- [Agnostic Tomography of Stabilizer Product States](https://mlsanity.com/paper/2404.03813/) (2024)
- [Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems](https://mlsanity.com/paper/2508.09103/) (2025)

## Abstract (arXiv)

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 mathfrakd, its Gibbs state at inverse temperature β, denoted by ρ = e-β H/ operatornametr(e-β H), is a classical distribution over product states for all β < 1/(cmathfrakd), 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 mathfrakd2), we can prepare a state varepsilon-close to ρ in trace distance with a depth-one quantum circuit and operatornamepoly(n, 1/varepsilon) classical overhead.