Research proof index

Definition of a CP map, but with Fintype T in the definition instead of a Fin n. -/ theorem of_Fintype {M : MatrixMap A B R} (h : IsCompletelyPositive M) (T : Type*) [Fintype T] [DecidableEq T] : (M.kron (LinearMap.id : MatrixMap T T R)).IsPositive := by obtain ⟨n, ⟨e⟩⟩ : ∃ n : ℕ, Nonempty (T ≃ Fin n) := Finite.exists_equiv_fin T convert h n using 1 h...

Definition of a CP map, but with Fintype T in the definition instead of a Fin n.

The dual of a IsPositive map also IsPositive.

The dual of a IsPositive map also IsPositive.

The composition of IsHermitianPreserving maps is also Hermitian preserving. -/ theorem comp {M₁ : MatrixMap A B R} {M₂ : MatrixMap B C R} (h₁ : M₁.IsHermitianPreserving) (h₂ : M₂.IsHermitianPreserving) : IsHermitianPreserving (M₂ ∘ₗ M₁) := fun _ h ↦ h₂ (h₁ h) end IsHermitianPreserving namespace IsPositive variable [Fintype A] [Fintype B] [Fintype C] /- Ev...

A map is trace preserving iff the partial trace of the Choi matrix is the identity.