Theorem · T-KLPR22-LEMMA5
Kent et al. 2022 · Methods
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
- Methods, Lemma 5, eqs.(12)-(16), PDF p.8; theoretical P_det eq.(17)
- Source file
- research/THEOREM_REGISTRY_SEED.yaml
Statement summary
Under assumptions E and F, reporting strategy 1 (QT1) and 2 (QT2) give report probabilities that factorise over pulses and don't depend on the measured basis. So the message m gives Bob no information about w_k for k with m_k = 1 (protection against arbitrary multi-photon attacks).
Citations
Record
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
Methods, Lemma 5, eqs.(12)-(16), PDF p.8; theoretical P_det eq.(17)
- Statusstatus
VERIFIED_FROM_SOURCE
- Formulas latexformulas_latex
eq12: P^{(1)}_{\mathrm{rep}}(m,w|\rho,L)=\prod_{k=1}^{N}G^{(1)}_{m_k,w_k}(d_0,d_1,\eta,L_k) eq13: G^{(1)}_{1,b}=(1-d_0)(1-d_1)(1-\eta/2)^{a}-(1-d_0)^2(1-d_1)^2(1-\eta)^{a};\ G^{(1)}_{0,0}=1-2G^{(1)}_{1,0};\ G^{(1)}_{0,1}=0 eq15: P^{(2)}_{\mathrm{rep}}(m|w,\rho,L)=\prod_{k=1}^{N}G^{(2)}_{m_k}(d_0,d_1,\eta,L_k) eq16: G^{(2)}_{0}=(1-d_0)(1-d_1)(1-\eta)^{a};\ G^{(2)}_{1}=1-(1-d_0)(1-d_1)(1-\eta)^{a} eq17: P^{\mathrm{theo}}_{\mathrm{det}}=2\left(e^{-\mu\eta/2}-e^{-\mu\eta}\right)=0.01863\ (\mu=0.09,\eta=0.21)- Verificationverification
statement_summary: VERIFIED_FROM_SOURCE formulas_latex: VERIFIED_FROM_SOURCE