费米子代数上作为径向乘子的若干信道的纠缠辅助经典容量
Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
AI总结：
本研究提出一类在有限维费米子代数上作为径向乘子的新型幺正量子信道，借助其与离散超立方体的关联，精确计算了共享无限纠缠时的经典信息传输速率，得到费米Ornstein-Uhlen半群算子的精确值，推进了量子信息论的维度无关研究。
摘要：
我们研究了矩阵代数$\n\t\t\t\t\t\t\t\mathrm{M}_{2^k}$上一类新的幺正量子信道，当将$\n\t\t\t\t\t\t\t\mathrm{M}_{2^k}$等同于有限维费米子代数时，这类信道可作为径向乘子发挥作用。我们的核心贡献是精确计算了发送方与接收方共享无限纠缠资源时，经典信息通过这些信道传输的（最优）速率。我们的方法基于费米子代数与n维离散超立方体$\n\t\t\t\t\t\t\t\{-1,1\}^n$之间的新关联。值得注意的是，我们的计算得到了适用于费米Ornstein-Uhlen半群算子的精确值。这一进展不仅深化了对这些信道结构与行为的认识，还提升了我们在维度无关语境下对量子信息论的理解。
英文摘要：
We investigate a new class of unital quantum channels on $\mathrm{M}_{2^k}$, acting as radial multipliers when we identify the matrix algebra $\mathrm{M}_{2^k}$ with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the $n$-dimensional discrete hypercube $\{-1,1\}^n$. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
