标题： 混合码 显示英文标题

标题： Hybrid Codes

摘要： 一种混合码可以同时将经典信息和量子信息编码到量子数字中，使得信息在通过量子信道传输时受到错误保护。 已经证明，一种混合码具有显著的特性，即它能够检测比能够编码经典和量子信息的可比较量子码更多的错误。 为混合码引入了重量枚举器，这些枚举器可用于表征混合码的最小距离。 令人惊讶的是，混合码的重量枚举器并不遵循通常的MacWilliams恒等式。 显示英文摘要

摘要： A hybrid code can simultaneously encode classical and quantum information into quantum digits such that the information is protected against errors when transmitted through a quantum channel. It is shown that a hybrid code has the remarkable feature that it can detect more errors than a comparable quantum code that is able to encode the classical and quantum information. Weight enumerators are introduced for hybrid codes that allow to characterize the minimum distance of hybrid codes. Surprisingly, the weight enumerators for hybrid codes do not obey the usual MacWilliams identity.