Multiplicative Semidefinite Programming Upper Bounds on Quantum No-Signalling-Assisted Zero-Error Capacity
The authors introduce a multiplicative semidefinite programming parameter, $\Gamma(K)$, that provides a tight upper bound for the asymptotic quantum no-signalling-assisted zero-error capacity, $\Theta_{\rm NS}(K)$. They prove this bound is the tightest among known SDP bounds and show that neither the simulation cost nor its regularized extension holds generally. Sharp bounds are derived for classical–quantum channels based on output dimension $r$ and minimum rank $k$, leading to a sharp operational estimate for the simulation gap.