On the One-Shot Zero-Error Classical Capacity of Classical-Quantum Channels Assisted by Quantum Non-signalling Correlations

Full metadata record
Files in This Item:
Filename Description Size
1504.06046v1.pdfSubmitted Version428.79 kB
Adobe PDF
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. 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 $\log \vartheta(G)$, where $\vartheta(G)$ is the celebrated Lov\'{a}sz theta function. 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 $\log \lfloor \vartheta(G) \rfloor$, which further implies that its asymptotic capacity is $\log \vartheta(G)$. 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. Examples of other graphs are also discussed. This endows the Lov\'{a}sz $\theta$ function with a more straightforward operational meaning.
Please use this identifier to cite or link to this item: