发表机构
International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk; Department of Computer Science, University of Oxford（格但斯克大学量子技术理论国际中心; 牛津大学计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过混合SU(3)表示中的两体控制，实现了无噪声子系统上的半通用酉门生成，并证明在相关噪声下编码的qutrit隐形传态可超越经典保真度界限1/2。
AI 中文摘要
集体噪声可以不影响某些自由度，使其能够存储量子信息。处理这些信息还需要物理上可用的逻辑门。我们考虑 $r$ 个基本 qutrit 在 $U\in SU(3)$ 下变换，以及 $s$ 个对偶 qutrit 在其复共轭 $\overline U$ 下变换，其集体作用为 $R_{r,s}(U)=U^{\otimes r}\otimes\overline U^{\otimes s}$。利用带墙的 Brauer 代数的像和李代数论证，我们证明了在每个 qutrit 类型内部的相邻交换以及两种类型之间的一个单重态投影相互作用，可以通过有限脉冲序列在无噪声子系统上生成任意独立选择的特殊酉门族，对于所有 $r,s\geq1$ 均成立。这确立了该系统的半通用性。我们通过一个数值优化的 24 脉冲序列（针对三个基本 qutrit 和一个对偶 qutrit）展示了该结果。然后，我们利用该编码和可用的逻辑校正，在相关 Weyl 噪声下进行 qutrit 隐形传态。在关于信道组成和保留哪些试验的明确假设下，并允许基线实现误差，我们确定了编码隐形传态超过经典保真度界限 $1/2$ 的噪声范围，而未编码的隐形传态信道是纠缠破坏的。我们分别分析接受试验上的保真度与额外物理 qutrit 的传输成本。
英文摘要
Collective noise can leave degrees of freedom unaffected, allowing them to store quantum information. Processing this information also requires physically available logical gates. We consider $r$ fundamental qutrits transforming under $U\in SU(3)$ and $s$ dual qutrits transforming under its complex conjugate $\overline U$, with collective action $R_{r,s}(U)=U^{\otimes r}\otimes\overline U^{\otimes s}$. Using the image of the walled Brauer algebra and Lie-algebra arguments, we show that adjacent exchanges within each qutrit type and one singlet-projector interaction between the two types generate any independently chosen family of special unitary gates on the noiseless subsystems by a finite pulse sequence, for every $r,s\geq1$. This establishes semi-universality of this system. We illustrate the result with a numerically optimised sequence of 24 pulses for three fundamental qutrits and one dual qutrit. We then use the encoding and available logical corrections for qutrit teleportation under correlated Weyl noise. Under explicit assumptions on channel composition and which trials are retained, and allowing for baseline implementation errors, we identify noise ranges in which encoded teleportation exceeds the classical fidelity bound of $1/2$, while the unencoded teleportation channel is entanglement breaking. We analyse fidelity on accepted trials separately from the transmission costs of the additional physical qutrits.
