We construct an explicit family of finite-dimensional quantum channels for which the optimal classical communication rate achievable with product-state codewords and collective decoding tends to zero, while rates achievable using entanglement only within pairs of channel inputs grow without bound. Our construction combines deterministic qudit Clifford unitaries with a binary measurement and classical feedforward, providing a derandomization to Hastings' probabilistic construction. The key ingredient is a careful design of measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.

翻译：暂无翻译