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Quantum Simulation
Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
arXiv
Authors: Tomotaka Kuwahara, Kohtaro Kato, Fernando G. S. L. Brandão
Year
2019
Paper ID
15416
Status
Preprint
Abstract Read
~2 min
Abstract Words
85
Citations
N/A
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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- 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...
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