Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature

Tomotaka Kuwahara; Kohtaro Kato; Fernando G. S. L. Brandão

doi:10.1103/physrevlett.124.220601

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arXiv · 1910.09425

Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature

Tomotaka Kuwahara·Kohtaro Kato·Fernando G. S. L. Brandão

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Abstract

We prove that the 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 demonstrate the exponential decay for short-ranged interacting systems and power-law decay for long-ranged interacting systems. Consequently, 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 simulations.

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quant-ph cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP

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Tomotaka Kuwahara, Kohtaro Kato, Fernando G. S. L. Brandão. 2020-06-02. Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature. https://doi.org/10.1103/physrevlett.124.220601

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