Invariants of the quantum graph of the partial trace

TL;DR

This paper analyzes key invariants of a specific quantum graph related to the partial trace quantum channel, providing exact computations of independence number, zero-error capacity, and Lovász functions.

Contribution

It introduces explicit calculations of important quantum graph invariants for the partial trace quantum channel, advancing understanding of quantum graph properties.

Findings

Computed independence number for the quantum graph

Determined zero-error capacity of the quantum graph

Evaluated Lovász and quantum Lovász functions

Abstract

We compute the independence number, zero-error capacity, and the values of the Lov\'asz function and the quantum Lov\'asz function for the quantum graph associated to the partial trace quantum channel $\operatorname{Tr}_n\otimes\mathrm{id}_k\colon\operatorname{B}(\mathbb{C}^n\otimes\mathbb{C}^k)\to\operatorname{B}(\mathbb{C}^k)$.