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Winter, "Improving zero-error classical communication with entanglement," Phys. Smith, "An extreme form of superactivation for quantum zero-error capacities," IEEE Trans. Harrow, "Superactivation of the asymptotic zero-error classical capacity of a quantum channel," IEEE Trans. Duan, "Super-activation of zero-error capacity of noisy quantum channel," 2009.

Shi, "Entanglement between two uses of a noisy multipartite quantum channel enables perfect transmission of classical information," Phys. Winter, "Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number," IEEE Trans. de Assis, "Quantum states characterization for the zero-error capacity," 2006. Haemers, "An upper bound for the Shannon capacity of a graph," Coll. Haemers, "On some problems of Lovász concerning the Shannon capacity of a graph," IEEE Trans. Lovász, "On the Shannon capacity of a graph," IEEE Trans. Shannon, "The zero error capacity of a noisy channel," IRE Trans. This gives Lovász v function another operational meaning in zero-error classical-quantum communication. Examples of other graphs are also discussed.

This type of graphs include the cycle graphs of odd length, the Paley graphs of prime vertices, and the cubit residue graphs of prime vertices. In this paper, we show that the one-shot capacity for a classical-quantum channel, induced from a circulant graph G defined by equal-sized cyclotomic cosets, is log, which further implies that its asymptotic capacity is log v(G). For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling correlations, minimized over all classical-quantum channels with a confusability graph G, is exactly log v(G), where v(G) is the celebrated Lovász theta function. Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel.