AI 中文总结
该研究针对分布式量子计算中多节点GKP态同态聚合问题，提出基于测量的有源框架，构建对应映射并证明其特性，推导了有限压缩下的保真度极限。
AI 中文摘要
聚合编码在连续变量相空间中的逻辑量子信息对分布式量子计算至关重要，但无源线性光学因辛晶格压缩和纠缠诱导的退相干，无法适用于非高斯Gottesman-Kitaev-Preskill（GKP）码。本文提出一种基于测量的有源框架，用于多节点GKP态的同态聚合；利用GKP贝尔态和零差前馈，构建完全正且迹保持的映射，计算分布式态的逻辑和，同时在可纠正的有限压缩变形范围内保留逻辑码空间几何。我们证明该协议作为近似量子非破坏测量运行，界定了其对连续一次性密钥的密码泄露，并推导了有限压缩约束下的解析逻辑保真度极限。
英文摘要
Aggregating logical information in continuous-variable quantum networks is essential for distributed quantum architecture. However, direct passive linear optics degrade non-Gaussian Gottesman-Kitaev-Preskill (GKP) grid states via symplectic lattice compression and entanglement-induced decoherence when auxiliary modes are discarded. We present an active, measurement-based continuous-variable network primitive for combining spatially distributed computational-basis payloads. Utilizing GKP Bell states, homodyne measurements, and conditional feed-forward phase-space displacements, we construct a completely positive trace-preserving (CPTP) map that evaluates a logical XOR operation on computational-basis inputs. We bound the Heisenberg action of the physical finite-squeezing channel on logical Pauli generators, demonstrate measurement-specific homodyne-outcome hiding for continuous-variable quantum one-time pads (CV-OTP) with an explicit prefactor bound $D_{\mathrm{TV}} \le 1.60 e^{-r}$, and evaluate logical success probabilities under physical optical loss and network scaling constraints.
Commentsv2: Major revision. 15 pages, 2 figures. Clarified protocol scope to computational-basis payloads (logical XOR), added explicit prefactor bound for cryptographic homodyne-hiding, and included the full phase-space symplectic derivation of the physical router
