A note on quantum expanders

TL;DR

This paper demonstrates that a broad class of sparse random quantum channels typically have a large spectral gap, making them effective quantum expanders, and provides a method to construct such expanders from classical counterparts.

Contribution

It introduces a new approach to construct quantum expanders from classical ones, expanding the known set of optimal quantum expanders.

Findings

Random quantum channels with few Kraus operators often have a large spectral gap.

The construction method links classical and quantum expanders.

The results rely on advanced random matrix theory techniques.

Abstract

We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In particular, our result provides a recipe to construct random quantum expanders from their classical (random or deterministic) counterparts. This considerably enlarges the list of known constructions of optimal quantum expanders, which was previously limited to few examples. Our proofs rely on recent progress in the study of the operator norm of random matrices with dependence and non-homogeneity, which we expect to have further applications in several areas of quantum information.