Highly entangled, non-random subspaces of tensor products from quantum groups

TL;DR

This paper explores highly entangled subspaces derived from quantum group representations, analyzing their properties and implications for quantum channels and positive maps in quantum information theory.

Contribution

It introduces a new class of entangled subspaces from quantum groups, characterizes their singular values, and links these to quantum channel entropy and positive map construction.

Findings

Determined largest singular values of the subspaces.

Provided lower bounds for minimum output entropy.

Constructed $d$-positive maps on matrix algebras.

Abstract

In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of $d$-positive maps on matrix algebras is also presented.