Freezing imaginarity of quantum states based on ℓ₁-norm

We discuss freezing of quantum imaginarity based on ℓ₁-norm. Several properties about a quantity of imaginarity based on ℓ₁-norm are revealed. For a qubit (2-dimensional) system, we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state. Furthermore, we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of N-qubit quantum states.