论文标题
对称古典量子通道的广义完美代码
Generalized Perfect Codes for Symmetric Classical-Quantum Channels
论文作者
论文摘要
我们为对称的经典量词渠道定义了一个新的代码家族，并建立了它们的最佳性。为此，我们将广义完美和准完美代码的经典概念扩展到在某些有限尺寸复杂的希尔伯特输出空间上定义的通道。所得的最优条件取决于所考虑的通道和通道输出空间上定义的辅助状态。对于某些$ n $ qubit的经典量词通道，我们表明基于铃铛状态的概括的代码是准完美的，因此它们具有相同的块长度和基数的所有代码之间的最小误差概率。
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain $N$-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.
