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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 $β$, denoted by $ρ=e^{-βH}/ \textrm{tr}(e^{-βH})$, is a classical distribution over product states for all $β< 1/(c\mathfrak{d})$, 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 $β< 1/( c \mathfrak{d}^3)$, we can prepare a state $ε$-close to $ρ$ in trace distance with a depth-one quantum circuit and $\textrm{poly}(n) \log(1/ε)$ 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.

View a PDF of the paper titled High-Temperature Gibbs States are Unentangled and Efficiently Preparable, by Ainesh Bakshi and 2 other authors This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states. 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.

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