Three-Point Quantum Identity Confirms Existing Performance Limits for GKP Error-Correcting Codes

Researchers have demonstrated an exact determination of the optimum for GKP lattice codes, revealing a surprising result: extending a quantum error-correction framework to incorporate three-point interactions yields no improvement over existing two-point methods. The work, led by Yinzi Xiao of Paderborn University’s Department of Computer Science, constructs a three-point continuous-variable quantum MacWilliams identity and explores its implications for code dimension and distance. This identity’s configuration space carries a symplectic invariant with no classical counterpart, encoding both the GKP quantization condition and a three-point sign phase. The team certifies a collapse of the three-point term for radial Choi forms on the first eight Laguerre levels…