High-Temperature Gibbs States are Unentangled and Efficiently Preparable

2024/03/25 by Ainesh Bakshi, Allen Liu, Allen P. Liu +6 · 4 voices · 18 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.2403.16850

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 \mathfrakd, 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/(c\mathfrakd), where c is a constant. This proof of sudden death of thermal entanglement resolves the fundamental question of whether many-body systems can exhibit entanglement at high temperature. Moreover, we show that we can efficiently sample from the distribution over product states. In particular, for any β< 1/( c \mathfrakd²), we can prepare a state ε-close to ρ in trace distance with a depth-one quantum circuit and poly(n, 1/ε) classical overhead.

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Discussions

• High-temperature Gibbs states are unentangled and efficiently preparable [hn, 80 points, 33 comments]
• Our third long plenary is an invited talk about High-temperature Gibbs states being unentangled and efficiently preparable (arxiv.org/abs/2403.16850 and related @quantamagazine.bsky.social coverage: t [bsky, 1 points, 0 comments]
• Indeed, it is quite well known that spin entanglement dies by heating and that above that temperature Gibbs states of many qubits are easy to prepare (see for instance the wonderful recent work by Ewi [bsky, 0 points, 1 comments]
• High-Temperature Gibbs States Are Unentangled and Efficiently Preparable (arxiv.org) Main Link | Discussion [bsky, 0 points, 0 comments]

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