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 d, its Gibbs state at inverse temperature β, denoted by ρ=e−βH/tr(e−βH), is a classical distribution over product states for all β<1/(cd), 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/(cd3), we can prepare a state ϵ-close to ρ in trace distance with a depth-one quantum circuit and 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."  

   

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