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cdec422 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | import OAI.InformationTheory.SecretKey.Model
import OAI.InformationTheory.DimensionTen.StateDensity
namespace OAI
/-! The normalized Choi state and key separation in the finite terminal-readout model. -/
noncomputable section
open Matrix
namespace ZeroKey.TenDimensional
universe u
def rho : Matrix (Fin 10 × Fin 10) (Fin 10 × Fin 10) ℂ :=
DimensionTen.rho
def MainClaim : Prop :=
∃ hR : Density rho, ¬ Separable rho ∧
(∀ u v : Fin 10 → ℂ, ∀ w : Fin 10 × Fin 10 → ℂ,
rho *ᵥ w = DimensionTen.productVector u v → u = 0 ∨ v = 0) ∧
distillableSecretKey.{u} rho hR = 0 ∧
UniformProtocolGap.{u} rho hR ∧ UniformCompletedGap.{u} rho hR
end ZeroKey.TenDimensional
end
end OAI
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