Time Travel, Quantum Entanglement and Quantum Computing

Part (i) Find the scalar product ⟨Ψ−(θ)∣Ψ+(θ)⟩\langle \Psi_{-}(\theta) | \Psi_{+}(\theta) \rangle⟨Ψ−​(θ)∣Ψ+​(θ)⟩ and discuss. Given: ∣Ψ+(θ)⟩=cos⁡(θ)∣0⟩+sin⁡(θ)∣1⟩|\Psi_{+}(\theta)\rangle = \cos(\theta) |0\rangle + \sin(\theta) |1\rangle∣Ψ+​(θ)⟩=cos(θ)∣0⟩+sin(θ)∣1⟩ ∣Ψ−(θ)⟩=cos⁡(θ)∣0⟩−sin⁡(θ)∣1⟩|\Psi_{-}(\theta)\rangle = \cos(\theta) |0\rangle - \sin(\theta) |1\rangle∣Ψ−​(θ)⟩=cos(θ)∣0⟩−sin(θ)∣1⟩ To find…