完美量子码的分类

Generalized Perfect Codes for Symmetric Classical-Quantum Channels

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 probabilit…

阿贝尔凯莱图上格罗弗游走中完美状态转移的完全分类

A complete classification of perfect state transfer in Grover walks on abelian Cayley graphs

该研究对有限阿贝尔群上表现出完美状态转移的连通凯莱图进行完全分类，确定其度数为1、2或4，给出度数为4时的充要条件，并将相关循环图分类结果扩展至任意有限阿贝尔群上的所有度数凯莱图。

在完美码中隐藏量子信息

Hiding Quantum Information in the Perfect Code

我们提出并分析了一个量子隐写协议，发送方（Alice）将她的隐写信息编码成完美（五量子比特）量子纠错码的错误伴随式，并通过去极化信道将其发送给接收方（Bob）。Alice和Bob共享一个经典的密钥，并以这样一种方式隐藏量子信息：对于无法访问密钥的窃听者（Eve）来说，量子信息看起来像是一个具有典型量子错误序列的无辜码字。我们计算的平均速率的关键消费，并显示该协议如何提高性能的信息分布在多个码字块。Alice和Bob利用不同的编码来优化他们可以发送给彼此的隐写比特的平均数量，同时匹配去极化信道的错误统计。

完美量子态分类的复杂性

The complexity of perfect quantum state classification

本文提出$k$-可学习性概念，证明判定$k$-可学习性可通过半定规划解决，给出固定$k$或固定维度时的多项式算法，并证明一般情形为NP-困难，刻画了完美量子态分类的复杂性边界。

No invariant perfect qubit codes

Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect. In this work, we present a number of general constraints for the layout of such invariant perfect tensors (IPTs) and further describe a systematic and constructive approach to check the existence of an IPT of given valence. We apply our algorithm to show that no…