Ordered-Angle Coding for Exact Multiuser Unanimity Testing
Abstract
We introduce ordered-angle coding for binary-unanimity testing among n transformation-only users in a serial quantum architecture inherited from Loop-Back communication. User Bi fixes one private sign across a logical word and applies R(siαj) in trial j. If w users choose the negative sign, serial composition gives R[(n−2w)αj]. We show that every fixed same-axis pulse that is deterministic for both unanimous inputs under the binary Bell readout has αj=qjπ/(2n) with integer qj. For a nonadaptive word q=(q1,…,qm), a mixed Hamming weight imitates the unanimous signature with probability Mq(w)=∏j=1mcos2 (πqjw/n). Within this complete deterministic-unanimity pulse family, a finite perfect word exists if and only if n is a power of two. For n=2r, the dyadic word (1,2,4,…,2r−1) is exact and pulse-minimal with mmin=r=log2n trials. It replaces the O(n2log(1/ε)) worst-case burden of repeated smallest-angle tests by exact O(log n) verification. Odd primes instead admit balanced statistical words with uniform mixed-weight imitation 2−(p−1). For actual operations R(siαj+δij), an ideal rejecting position is lifted to sin2Δj, where Δj=∑iδij. This yields explicit robustness bounds with angular and binary-readout errors. Bell entanglement is not required for the additive algebra, but it keeps the traveler locally maximally mixed in every honest trial. We therefore present the result as a coded multiuser relation primitive with optional raw conference-key-candidate use, not as a composably secure conference-key protocol.
Related
BibTeX
@misc{lizamaperez2026orderedangle,
title = {{Ordered-Angle Coding for Exact Multiuser Unanimity Testing}},
author = {Luis Adrián Lizama-Pérez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05645},
eprint = {2609.05645},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05645},
}
RIS
TY - UNPB
TI - Ordered-Angle Coding for Exact Multiuser Unanimity Testing
AU - Luis Adrián Lizama-Pérez
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05645
UR - https://arxiv.org/abs/2609.05645
AB - We introduce ordered-angle coding for binary-unanimity testing among n transformation-only users in a serial quantum architecture inherited from Loop-Back communication. User B_i fixes one private sign across a logical word and applies R(s_iα_j) in trial j. If w users choose the negative sign, serial composition gives R[(n−2w)α_j]. We show that every fixed same-axis pulse that is deterministic for both unanimous inputs under the binary Bell readout has α_j=q_jπ/(2n) with integer q_j. For a nonadaptive word q=(q_1,…,q_m), a mixed Hamming weight imitates the unanimous signature with probability M_q(w)=∏_j=1^mcos^2 (πq_jw/n). Within this complete deterministic-unanimity pulse family, a finite perfect word exists if and only if n is a power of two. For n=2^r, the dyadic word (1,2,4,…,2^r−1) is exact and pulse-minimal with m_min=r=log_2n trials. It replaces the O(n^2log(1/ε)) worst-case burden of repeated smallest-angle tests by exact O(log n) verification. Odd primes instead admit balanced statistical words with uniform mixed-weight imitation 2^−(p−1). For actual operations R(s_iα_j+δ_ij), an ideal rejecting position is lifted to sin^2Δ_j, where Δ_j=∑_iδ_ij. This yields explicit robustness bounds with angular and binary-readout errors. Bell entanglement is not required for the additive algebra, but it keeps the traveler locally maximally mixed in every honest trial. We therefore present the result as a coded multiuser relation primitive with optional raw conference-key-candidate use, not as a composably secure conference-key protocol.
ER -