Consider and

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

Consider ∣ψ⟩=12(∣0⟩+i∣1⟩)|\psi\rangle = \frac{1}{\sqrt2}(|0\rangle + i|1\rangle) and ∣ϕ⟩=12(∣0⟩−i∣1⟩)|\phi\rangle = \frac{1}{\sqrt2}(|0\rangle - i|1\rangle). Someone argues: "∣ϕ⟩|\phi\rangle differs from ∣ψ⟩|\psi\rangle only by turning ii into −i-i, and that is just a choice of overall phase convention, like writing −∣1⟩-|1\rangle instead of ∣1⟩|1\rangle. So ∣ϕ⟩|\phi\rangle and ∣ψ⟩|\psi\rangle are the same physical state and no measurement can tell them apart." ((a)) Find the error in this argument. ((b)) Give a measurement basis that distinguishes ∣ψ⟩|\psi\rangle and ∣ϕ⟩|\phi\rangle with certainty, and state the outcome probabilities it predicts for each state.

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