A qubit is in the mixed state .

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · Quantum states, measurement and entanglement

Quantum Information and Technology, Ch Mixed states, generalised measurement and telling states apart

Problem

A qubit is in the mixed state ρ=12(I+0.3X+0.4Z)\rho = \tfrac12(I + 0.3X + 0.4Z). ((a)) Compute the root fidelity F(ρ,∣0⟩⟨0∣)=⟨0∣ρ∣0⟩F(\rho, |0\rangle\langle0|) = \sqrt{\langle0|\rho|0\rangle}. ((b)) Compute the trace distance D(ρ,∣0⟩⟨0∣)D(\rho, |0\rangle\langle0|) from the Bloch vectors. ((c)) Check that the Fuchs-van de Graaf inequalities 1−F≤D≤1−F21-F \le D \le \sqrt{1-F^2} hold for these values.

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