 Solution

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

The Pauli Z gate gives a rotation through $π$ about the $z$ axis of the Bloch sphere. In Bloch vector coordinates,

(r_{x}, r_{y}, r_{z}) ⟼ (- r_{x}, - r_{y}, r_{z}) .

For example, this follows from

ZXZ = - X

Z Y Z = - Y

and

ZZZ = Z

in the Pauli matrix expansion

ρ = (I + r_{x} X + r_{y} Y + r_{z} Z) /2

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