耦合结构决定离散量子卷积信道中的通信机制
Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels
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中文总结 AI 辅助
本文研究离散量子卷积信道，发现耦合矩阵中单个零元素的位置决定两种通信机制：对角零导致纠缠破坏信道，非对角零导致可降解去相位信道，并给出相应容量公式。
中文摘要 AI 辅助
我们研究了近期发展的离散变量量子系统的量子卷积理论。我们根据耦合矩阵的哪些元素为零，对由可逆的$2\ imes2$耦合矩阵和固定环境态生成的离散量子卷积信道进行分类。在保持角色不变的基重新标记下，所有四个元素均非零的矩阵形成$d-2$个规范交比类，而恰好有一个元素为零的矩阵则分为四个不等价的支类。我们确定了所有四个单零元素支类的优化单发Holevo信息以及经典、量子和私有容量。如果对角元素为零，则该信道是纠缠破坏的测量-制备轨道信道：其经典容量等于环境态的相对熵相干性，而其量子和私有容量为零。如果非对角元素为零，则该信道是可降解的广义去相位信道：一个完整的正交归一基被无差错地传输，而量子和私有容量由环境态在共轭基下去相位后的熵亏确定。因此，单个零元素的位置选择了两种性质不同的通信机制。当所有四个元素均非零时，信道是不可约的Weyl协变的，将经典容量问题简化为正则化的最小输出熵问题。对于单qutrit情形中唯一的全非零耦合类，我们进一步推导了一个去极化单参数族的精确Holevo公式，并确定了其纠缠破坏阈值。
英文摘要
We study the recently developed theory of quantum convolution for discrete-variable quantum systems. We classify the discrete quantum convolutional channels generated by an invertible $2\times2$ coupling matrix and a fixed environmental state according to which entries of the coupling ma- trix vanish. Under role-preserving basis relabelings, matrices with all four entries nonzero form $d-2$ canonical cross-ratio classes, whereas matrices with exactly one vanishing entry split into four inequivalent branches. We determine the optimized one-shot Holevo information and the classical, quantum, and private capacities for all four one-entry-vanishing branches. If a diago- nal entry vanishes, the channel is an entanglement-breaking measure-and-prepare orbit channel: its classical capacity equals a relative entropy coherence of the environmental state, whereas its quantum and private capacities vanish. If an off-diagonal entry vanishes, the channel is a degradable generalized-dephasing channel: one complete orthonormal basis is transmitted without error, whereas the quantum and private capacities are determined by the entropy deficit of the environ-ental state after dephasing in the conjugate basis. Thus, the position of a single vanishing entry selects two qualitatively different communication regimes. When all four entries are nonzero, the channels are irreducibly Weyl covariant, reducing the classical-capacity problem to a regularized minimum-output-entropy problem. For the unique fully nonzero coupling class in the single-qutrit case, we further derive an exact Holevo formula for a depolarized one-parameter family and identify its entanglement-breaking threshold.
发表机构
- Central South University（中南大学）
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