 Solution

ID: past-exam-of-the-introduction-to-quantum-information-course-of-the-university-of-oxford/2021/3/c/i/solution

E_{r} (ρ) = \frac{1}{2} (I + r s \cdot σ), s ⟼ r s .

It contracts or expands every direction by the same factor and reverses the vector when

r < 0

. More generally

E_{r} (A) = r A + (1 - r) tr (A) I /2

, so the map preserves trace and Hermiticity for every real

r

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