University of Oulu

S. Alipour, S. Tuohino, A. T. Rezakhani, and T. Ala-Nissila, Unreliability of mutual information as a measure for variations in total correlations Phys. Rev. A 101, 042311 – Published 7 April 2020.-

Unreliability of mutual information as a measure for variations in total correlations

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Author: Alipour, S.1; Tuohino, S.2; Rezakhani, A. T.3;
Organizations: 1QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
2Faculty of Science, University of Oulu, 90570 Oulu, Finland
3Department of Physics, Sharif University of Technology, Tehran 14588, Iran
4Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, England, United Kingdom
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
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Language: English
Published: American Physical Society, 2020
Publish Date: 2020-06-03


Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both considered as proper measures of total correlations. We demonstrate that, when applied to the same system, these two measures can actually show significantly different behavior except at least in two limiting cases: when there are no correlations and when there is maximal quantum entanglement. We further quantify the discrepancy by providing analytic formulas for time derivatives of the measures for an interacting bipartite system evolving unitarily. We argue that to properly account for correlations one should consider the full information provided by the correlation matrix (and reduced states of the subsystems). Scalar quantities such as the norm of the correlation matrix or the quantum mutual information can only capture a part of the complex features of correlations. As a concrete example, we show that in describing heat exchange associated with correlations neither of these quantities can fully capture the underlying physics. As a byproduct, we also prove an area law for quantum mutual information in systems with local and short-range interactions, without need to assume Markovianity or final thermal equilibrium.

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Series: Physical review. A
ISSN: 2469-9926
ISSN-E: 2469-9934
ISSN-L: 2469-9926
Volume: 101
Issue: 4
Article number: 042311
DOI: 10.1103/PhysRevA.101.042311
Type of Publication: A1 Journal article – refereed
Field of Science: 114 Physical sciences
Funding: This work was supported by the Academy of Finland’s Center of Excellence program Quantum Technology Finland (QTF) Project No. 312298, Aalto University’s AScI Visiting Professor Funding, and Sharif University of Technology’s Office of Vice President for Research and Technology.
Copyright information: © 2020 American Physical Society.