Research proof index

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.

The kronecker product of IsTracePreserving maps is also trace preserving.

The map that takes M and returns M ⊗ₖ C, where C is positive semidefinite, is a completely positive map.