 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2019/4/e/ii/solution

Taking the partial trace over the left atom in the singlet state gives the right-hand reduced density matrix

(ρ_{R})_{s s^{'}} = \sum_{a =↑, ↓} ⟨ a, s ∣ ρ_{D} ∣ a, s^{'} ⟩, ρ_{R} = \frac{1}{2} (1001) = \frac{I}{2} .

Thus every measurement on the right stream alone has the same statistics as B or C. The joint pure state is compatible with locally mixed states; the correlations reside in the full density operator.

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