Statistical distribution of the local purity in a large quantum system

TL;DR

This paper extends the statistical analysis of local purity in large quantum systems from pure to mixed states, using a random matrix model and connecting to quantum channel theory, focusing on first moments due to computational complexity.

Contribution

It generalizes previous pure state analysis to mixed states and computes the first moments of local purity, linking to twirling maps in quantum channels.

Findings

Derived the first moments of local purity for mixed states.

Established a connection with twirling maps in quantum channels.

Extended the statistical mechanical approach to mixed states.

Abstract

The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be successful and a full characterization of the statistical properties of the local purity was obtained by computing the partition function of the problem. Here we generalize these techniques to the case of global mixed states. Since the computation of the partition function is far more challenging than in the pure case, we focus on the computation of the first moments of the local purity. Finally, we establish a connection with the theory of twirling maps in quantum channels.