Cooperation and dependencies in multipartite systems

• Main Authors: Klobus, Waldemar, Miller, Marek, Pandit, Mahasweta, Ganardi, Ray, Knips, Lukas, Dziewior, Jan, Meinecke, Jasmin, Weinfurter, Harald, Laskowski, Wieslaw, Paterek, Tomasz
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Quantum Information; Multipartite Entanglement
• Online Access: https://hdl.handle.net/10356/153876
• Institution: Nanyang Technological University

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.