稳定子子系统分解下高斯态的逻辑集合
The logical set of Gaussian states under the stabilizer subsystem decomposition
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中文总结 AI 辅助
该研究将高斯态映射到GKP逻辑子空间，通过稳定子子系统分解推导逻辑Bloch向量并刻画可达集，将几何框架转化为压缩见证认证工具，证明高斯态系综可违反稳定子界和经典界，分别认证集合魔法和密码学随机性。
中文摘要 AI 辅助
通用量子计算在连续变量系统中需要非高斯性，在离散变量系统中需要非稳定子性。然而，将高斯态映射到 Gottesman-Kitaev-Preskill 逻辑子空间可以产生具有非稳定子资源的逻辑量子比特。为了理解连续变量结构如何决定逻辑资源，我们刻画了单模高斯态在相应提取信道（即稳定子子系统分解）下的像。具体而言，我们推导了逻辑 Bloch 向量的级数表达式，并刻画了由此产生的可达集合，从而能够对逻辑态的魔法鲁棒性进行解析处理。然后，我们将这一几何框架转化为认证工具：通过将离散变量量子比特见证映射到连续变量压缩见证，我们获得了制备态压缩度的下界。我们还表明，高斯态系综可以违反稳定子界和经典界。违反稳定子界认证了称为“集合魔法”的关系资源，而违反经典界则能够在中等压缩度下认证密码学随机性。
英文摘要
Universal quantum computation requires non-Gaussianity in continuous-variable systems and non-stabilizerness in discrete-variable systems. Yet, mapping a Gaussian state into the Gottesman-Kitaev-Preskill logical subspace can yield a logical qubit with non-stabilizer resources. To understand how the continuous-variable structure determines logical resources, we characterize the image of single-mode Gaussian states under the corresponding extraction channel, known as the stabilizer subsystem decomposition. Specifically, we derive series expressions for the logical Bloch vector and characterize the resulting reachable set, enabling an analytical treatment of the robustness of magic of the logical states. We then turn this geometric framework into a certification tool: by mapping a discrete-variable qubit witness to a continuous-variable squeezing witness, we obtain lower bounds on the squeezing of prepared states. We also show that ensembles of Gaussian states can violate both stabilizer and classical bounds. Violation of the stabilizer bound certifies the relational resource known as "set-magic," while violation of the classical bound enables the certification of cryptographic randomness at moderate squeezing.
发表机构
- International Institute of Physics, Federal University of Rio Grande do Norte（联邦北里奥格兰德大学国际物理研究所）
- Physics Department, Federal University of Rio Grande do Norte（联邦北里奥格兰德大学物理系）
- Department of Mathematics and Statistics, University of Ottawa（渥太华大学数学与统计系）
- Center for Macroscopic Quantum States bigQ, Department of Physics, Technical University of Denmark（丹麦技术大学bigQ宏观量子态研究中心）
机构由 AI 辅助整理，请以论文原文为准。
