Theorem · T-JIANG24-THM1
Jiang et al. 2024 · Methods 'Security analysis'
P05 · arXiv v2 (2024-09-19); preprint, no journal reference on arXiv as of 2026-10-11
- Status
- VERIFIED FROM SOURCEField read in the primary source at the anchor given.VERIFIED_FROM_SOURCE; NOT_VERIFIED fields: P_MC_definition
- Game
- S2_JIANG24
- Anchor
- Methods 'Security analysis', Theorem 1, eqs.(22)-(25), arXiv v2 PDF p.17; parameter-confidence correction eqs.(26)-(29) p.18
- Source file
- research/THEOREM_REGISTRY_SEED.yaml
Statement summary
If max_{j,k} 2 P_MC(chi^k_j) < 1, N gamma_det <= n <= N, and 0 < P_noqub,theta < nu_unf < gamma_det (1 - gamma_err/(1 - P_bound)), with max 2 P_MC <= P_bound < 1, then eps_unf = sum_{l=0}^{floor(N(1-nu_unf))} C(N,l)(1-P_noqub,theta)^l P_noqub,theta^{N-l} + sum_{l=0}^{floor(n gamma_err)} C(n - floor(N nu_unf), l)(1-P_bound)^l P_bound^{n - floor(N nu_unf) - l}.
Citations
Record
Every field of the source record, in file order.
- Gamegame
S2_JIANG24
- Source paper idsource_paper_id
- P05
- Source urlsource_url
https://arxiv.org/abs/2408.13063
- Anchoranchor
Methods 'Security analysis', Theorem 1, eqs.(22)-(25), arXiv v2 PDF p.17; parameter-confidence correction eqs.(26)-(29) p.18
- Statusstatus
VERIFIED_FROM_SOURCE
- Reported valuesreported_values
- Recomputationrecomputation
RECOMPUTED_BY_LANE_A: eq.(28), 1-(1-P_wrong)^6 + eps_unf (1-P_wrong)^6 = 5.507e-9 (reported 5.52e-9). Eq.(27) with K=7 gives 1.82e-11 (reported 2.1e-11). The reported values are larger, so this looks like conservative rounding rather than an unsafe error. Flagged for lane D, not treated as an erratum.
- Verificationverification
statement_summary: VERIFIED_FROM_SOURCE reported_values: VERIFIED_FROM_SOURCE recomputation: RECOMPUTED_BY_LANE_A P_MC_definition: NOT_VERIFIED
- Not verified reasonsnot_verified_reasons
P_MC_definition: Lane A didn't transcribe the maximum-confidence quantities chi^k_j and eq.(4) P_noqub,theta from SI pages.