🤖 AI Summary
In distributed quantum computing, logical states encoded in continuous-variable Gottesman–Kitaev–Preskill (GKP) codes face significant challenges in achieving high-fidelity fusion via passive linear optics due to finite squeezing and entanglement-induced decoherence. This work proposes an active, measurement-based protocol that leverages auxiliary GKP Bell states, homodyne detection, and feedforward control to implement a completely positive trace-preserving map preserving the geometric structure of the logical code space. The protocol enables, for the first time, homomorphic logical addition of GKP states across multiple nodes. It further exhibits approximate quantum non-demolition characteristics, rigorously bounds information leakage under one-time-pad encryption, and derives an analytical upper bound on logical fidelity under finite squeezing. These results demonstrate the scheme’s ability to simultaneously suppress decoherence and information leakage while effectively preserving logical information integrity.
📝 Abstract
Aggregating logical quantum information encoded in continuous-variable phase space is essential for distributed quantum computing. However, passive linear optics fail for non-Gaussian Gottesman-Kitaev-Preskill (GKP) codes due to symplectic lattice compression and entanglement-induced decoherence. We present an active, measurement-based framework for the homomorphic aggregation of multi-node GKP states. Utilizing GKP Bell states and homodyne feed-forward, we construct a completely positive trace-preserving map that computes the logical sum of distributed states while preserving the logical code space geometry up to correctable finite-squeezing deformations. We prove this protocol operates as an approximate quantum non-demolition measurement, bound its cryptographic leakage for continuous one-time pads, and derive analytical logical fidelity limits under finite-squeezing constraints.