发表机构
Hanoi University of Science and Technology; National University of Singapore（河内科技大学; 新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对量子信道编码的最优成功概率计算难题，本文提出厄米平方和层级方法，证明其误差随层级二次收敛，并利用状态判别对偶性与正多项式核构造对偶证书，为二进制消息提供迹范数收缩系数的乘法近似上界。
AI 中文摘要
计算通过单次使用量子信道传输经典消息的最优成功概率是NP难的，即使对于两条消息也是如此。现有的基于对称扩展的半定规划层级提供了收敛的上界，其先验误差估计随扩展层级的平方根倒数衰减。在本工作中，我们为任意数量的消息构建了一个厄米平方和层级，并证明了其层级具有二次收敛性。误差界与相对于随机猜测的优势成正比。我们的方法将状态判别对偶性与球面乘积上的正多项式核相结合，以构造可行的多项式对偶证书。对于二进制消息，所得界给出了迹范数收缩系数的乘法近似上界。
英文摘要
Computing the optimal success probability for transmitting classical messages through a single use of a quantum channel is NP-hard, even for two messages. An existing semidefinite programming hierarchy based on symmetric extensions provides convergent upper bounds with an a priori error estimate that decays as the inverse square root of the extension level. In this work, we construct a Hermitian sum-of-squares hierarchy for an arbitrary number of messages and prove quadratic convergence in its level. The error bound is proportional to the advantage over random guessing. Our approach combines state-discrimination duality with positive polynomial kernels on products of spheres to construct feasible polynomial dual certificates. For binary messages, the resulting bounds give a multiplicative approximation from above of the trace-norm contraction coefficient.
