An electron spin qubit is prepared on the Bloch sphere at polar angle and azimuthal angle

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

Quantum Information and Technology, Ch Qubits, registers and the Bloch sphere

Problem

An electron spin qubit is prepared on the Bloch sphere at polar angle θ=60∘\theta = 60^\circ and azimuthal angle ϕ=90∘\phi = 90^\circ, using the parametrisation ∣ψ⟩=cos⁡(θ/2)∣0⟩+eiϕsin⁡(θ/2)∣1⟩|\psi\rangle = \cos(\theta/2)|0\rangle + e^{i\phi}\sin(\theta/2)|1\rangle, with ∣0⟩=∣↑z⟩|0\rangle = |{\uparrow_z}\rangle. ((a)) Write ∣ψ⟩|\psi\rangle in Dirac notation with numerical coefficients. ((b)) Find the probabilities of the two outcomes of a ZZ measurement. ((c)) Find the probabilities of the two outcomes of an XX measurement.

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