An extension of Bravyi-Smolin's construction for UMEBs

TL;DR

This paper generalizes a construction method for unextendible maximally entangled bases (UMEBs) using equiangular lines and projections, leading to new examples in many dimensions and confirming a conjecture about symmetric channels.

Contribution

It extends Bravyi and Smolin's UMEB construction to include equiangular real projections of higher rank, producing new UMEB examples in infinite dimensions.

Findings

New UMEB examples in infinitely many dimensions.

Validated conjecture on mixed unitary rank of symmetric Werner-Holevo channel.

Established orthogonal unitary bases for symmetric subspaces in odd dimensions.

Abstract

We extend Bravyi and Smolin's construction for obtaining unextendible maximally entangled bases (UMEBs) from equiangular lines. We show that equiangular real projections of rank more than 1 also exhibit examples of UMEBs. These projections arise in the context of optimal subspace packing in Grassmannian spaces. This generalization yields new examples of UMEBs in infinitely many dimensions of the underlying system. Consequently, we find a set of orthogonal unitary bases for symmetric subspaces of matrices in odd dimensions. This finding validates a recent conjecture about the mixed unitary rank of the symmetric Werner-Holevo channel in infinitely many dimensions.