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Clustering of Conditional Mutual Information for Quantum Gibbs States above a Threshold Temperature

Kuwahara, Tomotaka and Kato, Kohtaro and Brandão, Fernando G. S. L. (2020) Clustering of Conditional Mutual Information for Quantum Gibbs States above a Threshold Temperature. Physical Review Letters, 124 (22). Art. No. 220601. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20200601-141729048

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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 quasilocality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.124.220601DOIArticle
https://arxiv.org/abs/1910.09425arXivDiscussion Paper
ORCID:
AuthorORCID
Kuwahara, Tomotaka0000-0002-1612-3940
Kato, Kohtaro0000-0003-3317-2004
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2020 American Physical Society. Received 4 November 2019; revised manuscript received 31 January 2020; accepted 8 May 2020; published 1 June 2020. We thank Keiji Saito for valuable discussions on this work. The work of T. K. was supported by the RIKEN Center for AIP and JSPS KAKENHI Grant No. 18K13475. K. K. acknowledges funding provided by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center (NSF Grant No. PHY-1733907). F. B. is supported by the NSF.
Group:UNSPECIFIED, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
RIKEN UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)18K13475
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
Issue or Number:22
Record Number:CaltechAUTHORS:20200601-141729048
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200601-141729048
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103604
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Jun 2020 21:44
Last Modified:04 Jun 2020 10:35

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