| 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 | |