High-Temperature Gibbs States are Unentangled and Efficiently Preparable
<|reference_start|>High-Temperature Gibbs States are Unentangled and Efficiently Preparable: 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 $\rho =e^{-\beta H}/ \textrm{tr}(e^{-\beta H})$, is a classical distribution over product states for all $\beta < 1/(c\mathfrak{d})$, where $c$ is a constant. This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states.   Moreover, we show that we can efficiently sample from the distribution over product states. In particular, for any $\beta < 1/( c \mathfrak{d}^3)$, we can prepare a state $\epsilon$-close to $\rho$ in trace distance with a depth-one quantum circuit and $\textrm{poly}(n) \log(1/\epsilon)$ classical overhead. A priori the task of preparing a Gibbs state is a natural candidate for achieving super-polynomial quantum speedups, but our results rule out this possibility above a fixed constant temperature.<|reference_end|>
@article{bakshi2024high-temperature,
    title={High-Temperature Gibbs States are Unentangled and Efficiently Preparable},
    author={Ainesh Bakshi, Allen Liu, Ankur Moitra and Ewin Tang},
    journal={arXiv preprint arXiv:2403.16850},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16850},
    primaryClass={quant-ph cs.DS math-ph math.MP}
}