Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published June 5, 2020 | Supplemental Material + Submitted + Published
Journal Article Open

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

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.

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.

Attached Files

Published - PhysRevLett.124.220601.pdf

Submitted - 1910.09425.pdf

Supplemental Material - Markov_supplemental.pdf

Files

Markov_supplemental.pdf
Files (2.3 MB)
Name Size Download all
md5:6609d13dd2335dd112b7faad05f8a9e9
632.1 kB Preview Download
md5:1d1832827d7fdac3f2f869ba3c3da588
1.3 MB Preview Download
md5:efa176b1af0250e2944abcaaa7204fb8
328.4 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023