For with four equally spaced settings separated by an angle

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · Quantum states, measurement and entanglement

Quantum Information and Technology, Ch Nonlocality: EPR, Bell inequalities and the CHSH game

Problem

For ∣Φ+⟩|\Phi^+\rangle with four equally spaced settings separated by an angle θ\theta, the CHSH combination is S(θ)=3cos⁡θ−cos⁡3θS(\theta) = 3\cos\theta - \cos3\theta. ((a)) Evaluate S(θ)S(\theta) at θ=60∘\theta = 60^\circ. ((b)) State whether this value violates the local bound ∣S∣≤2|S|\le2, and compute the corresponding CHSH game winning probability pwin=12+S/8p_{\rm win} = \tfrac12 + S/8.

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