Quantum Information course of the University of Oxford Hilary 2023 problem sheet

Quantum Information course of the University of Oxford Hilary 2023 problem sheet 1

C^{2}

∣ ∣ ψ ⟩ ∣ = ∣ ∣ ∣ \frac{1 + i}{2} ∣ ∣ ∣^{2} + ∣ ∣ ∣ \frac{1 - i}{2} ∣ ∣ ∣^{2} = ∣ ∣ ∣ \frac{1}{2} + i \frac{1}{2} ∣ ∣ ∣^{2} + ∣ ∣ ∣ \frac{1}{2} + i \frac{- i}{2} ∣ ∣ ∣^{2} = (\frac{1}{2})^{2} + (\frac{1}{2})^{2}^{2} + (\frac{1}{2})^{2} + (\frac{- 1}{2})^{2}^{2} = (\frac{1}{2})^{2} + (\frac{1}{2})^{2} + (\frac{1}{2})^{2} + (\frac{- 1}{2})^{2} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + = \frac{1 + 1 + 1 + 1}{4} = 1

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