Cooperation and dependencies in multipartite systems
Abstract
We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations.
Cite
@article{arxiv.2003.12489,
title = {Cooperation and dependencies in multipartite systems},
author = {Waldemar Klobus and Marek Miller and Mahasweta Pandit and Ray Ganardi and Lukas Knips and Jan Dziewior and Jasmin Meinecke and Harald Weinfurter and Wieslaw Laskowski and Tomasz Paterek},
journal= {arXiv preprint arXiv:2003.12489},
year = {2021}
}
Comments
9 pages, journal version