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arXiv · 1608.04508

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

Xin Wang·Runyao Duan
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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.

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Xin Wang, Runyao Duan. 2018-01-18. Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity. https://doi.org/10.1109/tit.2018.2794391

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