Theorem · T-KLPR22-LEMMA3

Kent et al. 2022 · Lemma 3

P03 · npj Quantum Inf. 8, 28 (published 2022-03-11); equations transcribed from the article HTML TeX source

Status: VERIFIED FROM SOURCEField read in the primary source at the anchor given.
Game: S2
Anchor: Lemma 3, eqs.(4)-(5), main text PDF p.5-6; proof Supplementary Note V
Source file: research/THEOREM_REGISTRY_SEED.yaml

Statement summary

If (4) holds, QT1 and QT2 are eps_cor-correct with (5).

Citations

Every field of the source record, in file order.

Proof obligationproof_obligation: P-S2
Gamegame: S2
Source paper idsource_paper_id: P03
Source urlsource_url: https://doi.org/10.1038/s41534-022-00524-4
Anchoranchor: Lemma 3, eqs.(4)-(5), main text PDF p.5-6; proof Supplementary Note V
Statusstatus: VERIFIED_FROM_SOURCE
Preconditions latexpreconditions_latex: 0<\frac{\gamma_{\mathrm{err}}}{2}<E<\gamma_{\mathrm{err}}
0<\nu_{\mathrm{cor}}<\frac{P_{\mathrm{det}}(1-2\beta_{\mathrm{PB}})}{2}
Bound latexbound_latex: \epsilon_{\mathrm{cor}}=e^{-\frac{P_{\mathrm{det}}(1-2\beta_{\mathrm{PB}})N}{4}\left(1-\frac{2\nu_{\mathrm{cor}}}{P_{\mathrm{det}}(1-2\beta_{\mathrm{PB}})}\right)^{2}}+e^{-\frac{E\nu_{\mathrm{cor}}N}{3}\left(\frac{\gamma_{\mathrm{err}}}{E}-1\right)^{2}}
LaTeX source
Bound plainbound_plain: exp(-(P_det*(1-2*beta_PB)*N/4)*(1 - 2*nu_cor/(P_det*(1-2*beta_PB)))**2) + exp(-(E*nu_cor*N/3)*(gamma_err/E - 1)**2)
Variablesvariables
Caveatcaveat: As transcribed, precondition (4) requires E > gamma_err/2. That is what the source says (TeX from the article HTML). Don't 'fix' it.
Verificationverification: statement_summary: VERIFIED_FROM_SOURCE preconditions_latex: VERIFIED_FROM_SOURCE bound_latex: VERIFIED_FROM_SOURCE