Quantum partial information decomposition

Partial information decomposition (PID) takes one step beyond Shannon's theory in decomposing the information two variables, A and B, possess about a third variable, T, into distinct parts: unique, shared (or redundant), and synergistic information. Here we show how these concepts can be defined in a quantum setting. We apply a quantum PID to scrambling in quantum many -body systems, for which a quantum -theoretic description has been proven to be productive. Unique information in particular provides a finer description of scrambling than does the so-called tri-information.