TY - JOUR

T1 - On the one-shot zero-error classical capacity of classical-quantum channels assisted by quantum non-signalling correlations

AU - Lai, Ching-Yi

AU - Duan, Runyao

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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 classicalquantum channels with a confusability graph G, is exactly log v(G), where v(G) is the celebrated Lovász 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⌊v(G)⌋, which further implies that its asymptotic capacity is log v(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 gives Lovász v function another operational meaning in zero-error classical-quantum communication.

AB - 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 classicalquantum channels with a confusability graph G, is exactly log v(G), where v(G) is the celebrated Lovász 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⌊v(G)⌋, which further implies that its asymptotic capacity is log v(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 gives Lovász v function another operational meaning in zero-error classical-quantum communication.

KW - Lovász v function

KW - Non-signalling correlation

KW - Zero-error capacity

UR - http://www.scopus.com/inward/record.url?scp=85019157592&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85019157592

VL - 17

SP - 380

EP - 398

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 5-6

ER -