High-Temperature Gibbs States are Unentangled and Efficiently Preparable
AI Breakdown
Get a structured breakdown of this paper — what it's about, the core idea, and key takeaways for the field.
Abstract
We show that thermal states of local Hamiltonians are separable above a constant temperature. Specifically, for a local Hamiltonian <tex>$H$</tex> on a graph with degree <tex>$\mathfrak{g}$</tex>, its Gibbs state at inverse temperature <tex>$\beta$</tex>, denoted by <tex>$\rho=e^{-\beta H}/\text{tr}(e^{-\beta H})$</tex>, is a classical distribution over product states for all <tex>$\beta < 1/ (c \mathfrak{{g}})$</tex>, where <tex>$c$</tex> 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 <tex>$\beta < 1/(c\mathfrak{g}^{3})$</tex>, we can prepare a state <tex>$\varepsilon$</tex> -close to <tex>$\rho$</tex> in trace distance with a depth-one quantum circuit and <tex>$\text{poly}(n)\log(1/\varepsilon)$</tex> classical overhead. <sup>1</sup><sup>1</sup> In independent and concurrent work, Rouzé, França, and Alhambra [37] obtain an efficient quantum algorithm for preparing high-temperature Gibbs states via a dissipative evolution.