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This research introduces an active, measurement-based protocol for aggregating logical information in continuous-variable quantum networks using Gottesman-Kitaev-Preskill states. By employing homodyne measurements and conditional feed-forward displacements, the study achieves a robust logical XOR operation while providing explicit bounds on decoherence under optical loss and scaling constraints. The work advances distributed quantum architecture by addressing critical issues of state degradation inherent in passive linear optics for non-Gaussian grid states.
Homomorphic Aggregation of Continuous-Variable GKP States
arXiv:2608.13227v2 Announce Type: replace 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.
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.
v2: 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
Quantum Physics (quant-ph); Cryptography and Security (cs.CR)
arXiv:2608.13227 [quant-ph]
(or arXiv:2608.13227v2 [quant-ph] for this version)
From: Nilesh Vyas Dr. [view email] [v1] Thu, 13 Aug 2026 13:30:11 UTC (436 KB) [v2] Mon, 17 Aug 2026 12:33:39 UTC (1,559 KB)
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