Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity

Abstract

Quantum Lovász number is a quantum generalization of the Lovász 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 Lovász 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 Lovász 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.

v3 is closed to the published version; v2 improved the presentation

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Cited by in corpus (3)

• Non-asymptotic entanglement distillation
• Generic nonadditivity of quantum capacity in simple channels
• The platypus of the quantum channel zoo