Homomorphic Aggregation of Continuous-Variable GKP States

• URL: http://arxiv.org/abs/2608.13227v2
• Date: Mon, 17 Aug 2026 12:33:39 GMT
• Title: Homomorphic Aggregation of Continuous-Variable GKP States
• Abstract summary: Direct passive linear optics degrade non-Gaussian Gottesman-Kitaev-Preskill grid states.<n>We present an active, measurement-based continuous-variable network primitive for combining spatially distributed payloads.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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