Completing bases in four dimensions

TL;DR

This paper presents criteria and constructive methods for completing incomplete bases in four-dimensional Hilbert spaces using (in)decomposable vectors, advancing the understanding of basis completion in quantum and mathematical contexts.

Contribution

It introduces new criteria and methods specifically for completing bases in four-dimensional Hilbert spaces with (in)decomposable vectors.

Findings

Provides explicit criteria for basis completion.

Develops constructive methods for basis extension.

Enhances understanding of vector decomposability in basis completion.

Abstract

Criteria and constructive methods for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.