 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/3/c/ii/solution

The state is separable. The off-diagonal terms of the two Bell state projectors have opposite signs and cancel:

\frac{1}{2} ∣ ϕ_{+} ⟩ ⟨ ϕ_{+} ∣ + \frac{1}{2} ∣ ϕ_{-} ⟩ ⟨ ϕ_{-} ∣ = \frac{1}{2} ∣00 ⟩ ⟨ 00∣ + \frac{1}{2} ∣11 ⟩ ⟨ 11∣.

1/2

each, establishing a separable quantum state. Its correlations are classical; an ensemble decomposition into entangled states does not itself establish quantum entanglement of the density matrix.

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