A generalized infinite quantum Ramsey theorem for operator systems

TL;DR

This paper generalizes the infinite quantum Ramsey theorem by demonstrating it follows from a specific pattern of projections in infinite-dimensional Hilbert spaces.

Contribution

It introduces a broad generalization of the quantum Ramsey theorem based on a new archetypical pattern of projections.

Findings

The generalized theorem applies to a wider class of operator systems.

It identifies a selective pattern in projections that underpins the theorem.

The approach simplifies understanding of infinite quantum combinatorial principles.

Abstract

We prove a generalization of the infinite quantum Ramsey theorem of Kennedy et al. (arXiv:1711.09526), showing that it follows from an archetypical "selective" pattern satisfied by certain families of projections in an infinite-dimensional Hilbert space.