A transference method in quantum probability

TL;DR

This paper introduces a transference method in quantum probability that compares p-norms of sums of independent and free copies, leveraging operator space embeddings to connect noncommutative inequalities and Lp embedding theory.

Contribution

It develops a novel transference technique using explicit operator space embeddings to relate different notions of independence in quantum probability.

Findings

Established a method to compare p-norms of sums of independent and free copies.

Applied the technique to noncommutative Khintchine and Rosenthal inequalities.

Provided insights into noncommutative Lp embedding theory.

Abstract

Working with a rather general notion of independence, we provide a transference method which allows to compare the p-norm of sums of independent copies with the p-norm of sums of free copies. Our main technique is to construct explicit operator space Lp embeddings preserving independence to reduce the problem to L1, where some recent results by the first-named author can be used. We find applications for noncommutative Khincthine/Rosenthal type inequalities and for noncommutative Lp embedding theory.