 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/quantum-information/3/c/i/solution

The sign factor separates as

(- 1)^{x + y} = (- 1)^{x} (- 1)^{y}

\frac{1}{2} \sum_{x, y = 0}^{1} (- 1)^{x + y} ∣ x ⟩ ∣ y ⟩ = (\frac{∣0 ⟩ - ∣1 ⟩}{2}) \otimes (\frac{∣0 ⟩ - ∣1 ⟩}{2}) = ∣ - ⟩ \otimes ∣ - ⟩ .

It is a product state, so it is not entangled.

 New to topics? Read the docs here!