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
A single-photon qubit is prepared, before normalisation, as ∣ψ⟩∝2∣0⟩+(1−i)∣1⟩, where ∣0⟩ is horizontal polarisation and ∣1⟩ is vertical.
((a)) Normalise the state.
((b)) Find the probabilities of the two outcomes of a measurement in the {∣0⟩,∣1⟩} basis.
((c)) Compute the Bloch vector (⟨X⟩,⟨Y⟩,⟨Z⟩).
((d)) Find the probability of the + outcome of a measurement in the {∣+⟩,∣−⟩} basis.