High-Temperature Gibbs States are Unentangled and Efficiently Preparable

• URL: http://arxiv.org/abs/2403.16850v1
• Date: Mon, 25 Mar 2024 15:11:26 GMT
• Title: High-Temperature Gibbs States are Unentangled and Efficiently Preparable
• Authors: Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang,
• Abstract summary: We show that thermal states of local Hamiltonians are separable above a constant temperature. This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states.
• Score: 22.397920564324973
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathfrak{d}$, 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.

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