对易子几何与量子开关中的信息保持
Commutator Geometry and Information Preservation in the Quantum Switch
- School of Sciences, Hebei University of Science and Technology（河北科技大学理学院）
- Network Management Center, China Mobile Communications Group Hebei Co., Ltd.（中国移动通信集团河北有限公司网络管理中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究探讨量子开关在对易信道中如何影响信息保持，发现其对某些态族在保真度、可区分性和Fisher信息上优于或等同于固定顺序，并揭示了对易子几何与逻辑错误结构的作用。
AI中文摘要：
两个对易信道在任一固定顺序下产生相同的复合信道，但它们的量子开关可以改变信息保持。我们研究了这种效应如何依赖于输入态，并保留控制位和目标位的联合输出。精确的Kraus对易子恒等式确定了重叠度和保真度平方的差距。固定顺序在保真度上至少与开关一样好地保持乘积输入。对于两个量子比特的纯态，若其控制Schmidt基可选择为与顺序基一致，则反向不等式成立。一个对易子矩阵确定了在该对齐族中固定纠缠下最大化保真度平方差距的目标基。对于具有相等错误概率的Pauli $X$和$Y$信道，开关将逻辑相位翻转替换为一个稳定联合码的算子。在固定噪声下，对于该码中的每个态族，开关至少保持与固定顺序一样多的可区分性和量子Fisher信息。对于此处研究的纯编码族，精确公式将相位信息增益与保真度平方差距联系起来，并量化了关于噪声概率信息的减少。优化探针在两种联合信道下产生相等的最大量子Fisher信息用于噪声估计。这些结果将对易子几何和逻辑错误结构与态保持及编码信息的保留联系起来。
英文摘要：
Two commuting channels yield the same composite channel in either fixed order, yet their quantum switch can alter information preservation. We study how this effect depends on the input state, retaining the joint output of the control and target. Exact Kraus commutator identities determine overlap and squared fidelity gaps. Fixed order preserves product inputs at least as well as the switch in fidelity. The reverse inequality holds for pure states of two qubits whose control Schmidt basis can be chosen to coincide with the order basis. A commutator matrix determines the target basis that maximizes the squared fidelity gap at fixed entanglement within this aligned family. For Pauli $X$ and $Y$ channels with equal error probabilities, the switch replaces a logical phase flip with an operator that stabilizes a joint code. At fixed noise, the switch preserves at least as much distinguishability and quantum Fisher information as fixed order for every state family in this code. For the pure encoded family studied here, exact formulas connect the phase information gain to the squared fidelity gap and quantify the reduction in information about the noise probability. Optimizing the probes yields equal maximal quantum Fisher information for noise estimation under both joint channels. These results connect commutator geometry and logical error structure to state preservation and the retention of encoded information.
