Separation between quantum Lov\'asz number and entanglement-assisted zero-error classical capacity

TL;DR

This paper demonstrates a strict separation between the quantum Lovász number and the entanglement-assisted zero-error classical capacity using specially constructed qutrit channels, revealing limits of entanglement's enhancement.

Contribution

It constructs specific quantum channels showing a gap between the quantum Lovász number and actual zero-error capacity, advancing understanding of quantum channel capacities.

Findings

Existence of a strict gap between quantum Lovász number and entanglement-assisted capacity.

Quantum fractional packing number can exceed zero-error capacity with feedback or no-signalling.

Classical analogs differ from quantum cases in capacity bounds.

Abstract

Quantum Lov\'asz number is a quantum generalization of the Lov\'asz number in graph theory. It is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains an intriguing open problem whether quantum entanglement can always enhance the zero-error capacity to achieve the quantum Lov\'asz number. In this paper, by constructing a particular class of qutrit-to-qutrit channels, we show that there exists a strict gap between the entanglement-assisted zero-error capacity and the quantum Lov\'asz number. Interestingly, for this class of quantum channels, the quantum generalization of fractional packing number is strictly larger than the zero-error capacity assisted with feedback or no-signalling correlations, which differs from the case of classical channels.