PreprintCC BY 4.0arXiv
Lattice moments and quantum designs
Abstract
We show that the ensemble of unimodular Gottesman−Kitaev−Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure. This is established by rederiving a second moment formula for symplectic lattices in a self-contained manner.
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BibTeX
@misc{conrad2026lattice,
title = {{Lattice moments and quantum designs}},
author = {Jonathan Conrad and Kristian Holm},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40481},
eprint = {2610.40481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40481},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lattice moments and quantum designs
AU - Jonathan Conrad
AU - Kristian Holm
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40481
UR - https://arxiv.org/abs/2610.40481
AB - We show that the ensemble of unimodular Gottesman−Kitaev−Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure. This is established by rederiving a second moment formula for symplectic lattices in a self-contained manner.
ER -