All $S_p$ notions of quantum expansion are equivalent

TL;DR

This paper proves that all $S_p$-based quantum expansion notions are equivalent, resolving an open question in the field.

Contribution

It establishes the equivalence of various $S_p$-based quantum expansion notions, providing a unified understanding.

Findings

All $S_p$ notions of quantum expansion are equivalent

Resolved an open question in quantum expansion theory

Simplifies the conceptual framework of quantum expansion

Abstract

In a recent work Li, Qiao, Wigderson, Wigderson and Zhang introduced notions of quantum expansion based on $S_p$ norms and posed as an open question if they were all equivalent. We give an affirmative answer to this question.