Continuous Non-Archimedean and p-adic Welch Bounds

TL;DR

This paper extends Welch bounds to continuous non-Archimedean and p-adic Banach and Hilbert spaces, proposing new conjectures in these mathematical frameworks.

Contribution

It introduces continuous non-Archimedean and p-adic Welch bounds and formulates related functional Zauner conjectures, advancing the theory in these areas.

Findings

Proved continuous non-Archimedean Welch bounds.

Proved continuous p-adic Welch bounds.

Formulated non-Archimedean and p-adic Zauner conjectures.

Abstract

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate continuous non-Archimedean and p-adic functional Zauner conjectures.