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
Two superconducting (transmon) qubits, labelled 1 and 2, are prepared, before normalisation, in the state ∣ϕ⟩∝∣00⟩+∣01⟩+2∣11⟩.
((a)) Normalise the state.
((b)) Qubit 1 is measured in the computational basis. Find the probability of each outcome and the state left on qubit 2 in each case.
((c)) Find the probability that qubit 2, if it alone were measured in the computational basis, gives outcome 1, and check that it agrees with the value obtained by combining the two outcomes of part (b) with the law of total probability.