Quantum Partial Information Decomposition

TL;DR

This paper extends the concept of Partial Information Decomposition to quantum systems, providing a new framework for analyzing information sharing and scrambling in quantum many-body systems.

Contribution

It introduces a quantum version of PID and demonstrates its application to quantum scrambling, offering a more detailed understanding than previous measures.

Findings

Quantum PID can distinguish different types of information in quantum systems.

Application to quantum many-body systems reveals finer details of information scrambling.

Quantum PID outperforms traditional measures like tri-information in certain scenarios.

Abstract

The Partial Information Decomposition (PID) takes one step beyond Shannon's theory in decomposing the information two variables $A,B$ 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 productive. Unique information in particular provides a finer description of scrambling than does the so-called tri-information.