Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 3 / c / i

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- Solution i

Solution

The sign factor separates as

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

. Consequently the quantum state factors into a tensor product of quantum systems:

\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.

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