Correlation function and mutual information

Dong, Ruige; Zhou, D. L.

doi:10.1088/1751-8113/43/44/445302

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…Mainly, we consider correlation and independence information. These concepts have profound implications in the physical [ Dong and Zhou , 2010; Peleg et al , 2010] and information science fields [ Cover and Thomas , 2006; Papoulis , 1991]. We shortly describe these concepts for efficiently combine multimodel ensemble data.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Mainly, we consider correlation and independence information. These concepts have profound implications in the physical [Dong and Zhou, 2010;Peleg et al, 2010] and information science fields The last column (FOEX) gives the percentage of over-prediction (>0) or under-predictions (<0). In the next to last row, Median Model results, averaged over models from m01 to m16 (following Galmarini et al [2004b]) are shown.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling

Riccio¹,

Ciaramella²,

Giunta³

et al. 2012

J. Geophys. Res.

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[1] The aim of this work is to explore the effectiveness of theoretical information approaches for the reduction of data complexity in multimodel ensemble systems. We first exploit a weak form of independence, i.e. uncorrelation, as a mechanism for detecting linear relationships. Then, stronger and more general forms of independence measure, such as mutual information, are used to investigate dependence structures for model selection. A distance matrix, measuring the interdependence between data, is derived for the investigated measures, with the scope of clustering correlated/dependent models together. Redundant information is discarded by selecting a few representative models from each cluster. We apply the clustering analysis in the context of atmospheric dispersion modeling, by using the ETEX-1 data set. We show how the selection of a small subset of models, according to uncorrelation or mutual information distance criteria, usually suffices to achieve a statistical performance comparable to, or even better than, that achieved from the whole ensemble data set, thus providing a simpler description of ensemble results without sacrificing accuracy.Citation: Riccio A., A. Ciaramella, G. Giunta, S. Galmarini, E. Solazzo, and S. Potempski (2012), On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling,

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Section: Theoretical Backgroundmentioning

confidence: 99%

“…Mainly, we consider correlation and independence information. These concepts have profound implications in the physical [Dong and Zhou, 2010;Peleg et al, 2010] and information science fields The last column (FOEX) gives the percentage of over-prediction (>0) or under-predictions (<0). In the next to last row, Median Model results, averaged over models from m01 to m16 (following Galmarini et al [2004b]) are shown.…”

Section: Introductionmentioning

confidence: 99%

On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling

Riccio¹,

Ciaramella²,

Giunta³

et al. 2012

J. Geophys. Res.

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“…On one hand, by analogy with the concept of correlation functions for describing correlation effects in many-body physics [28] and taking into account that correlation functions are directly related to observables [28], it can be verified that the information related to both, classical and quantum correlations present in the composite quantum system, is in fact contained inside the elements T ij of the correlation matrix T. This matrix was used to investigate, for example, the dynamics of open quantum systems in the presence of initial correlations [29], and to study correlations in the quantum state of a composite system [30,31].…”

Section: A Quantum Discordmentioning

confidence: 99%

Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

Bussandri

Osán

Majtey

et al. 2020

Physica A: Statistical Mechanics and its Applications

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In this paper we use the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. To illustrate the use of this matrix, we analyze the behavior of the correlations under non-dissipative decoherence in two-qubit states with maximally mixed marginals. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in the Bell-diagonal states. In addition, we use the correlation matrix to study the phenomenon known as freezing of quantum discord. We find that under some initial conditions where freezing of quantum discord takes place, quantum correlation instead may remain not constant. In order to further explore into these results we also compute a non-commutativity measure of quantum correlations to analyze the behavior of quantum correlations under non-dissipative decoherence. We conclude from our study that freezing of quantum discord may not always be identified as equivalent to the freezing of the actual quantum correlations.

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“…QMI has various appealing properties and also admits diverse operational interpretations, e.g., as the amount of noise required to completely destroy all correlations [27][28][29]. Notwithstanding, there also exist observations showing incompatibilities between some measures of the total, classical, and quantum correlations [30][31][32][33] as opposed to what had been largely accepted, which indicate that QMI or other mea-sures of entanglement and quantumness of correlations may not be compatible for ordering quantum states based on the amount of correlations they contain [34]. In a broader context, it has been known in (quantum) resource theory that some resources are not totally ordered sets; see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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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Correlation function and mutual information

Cited by 9 publications

References 22 publications

On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling

On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling

Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

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

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