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28 March 2024
 
  » arxiv » 1910.9425

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Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
Tomotaka Kuwahara ; Kohtaro Kato ; Fernando G. S. L. Brandão ;
Date 21 Oct 2019
AbstractWe prove that quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We prove exponential decay (power-law decay) for short-ranged (long-ranged) interacting systems. As consequences, we establish the efficiency of quantum Gibbs sampling algorithms, a strong version of the area law, the quasi-locality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulation.
Source arXiv, 1910.9425
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