Bad Qubits — Learn Quantum by Doing

Multiple choice

In the CHSH game the players share a Bell pair and measure along angles set by their inputs: Alice uses

\alpha = \{0, \pi/2\}

for

x = \{0,1\}

, Bob uses

\beta = \{\pi/4, -\pi/4\}

for

y = \{0,1\}

. For inputs

(x,y)

the probability their outcomes agree is

\cos^2((\alpha_x - \beta_y)/2)

. They need agreement unless

x

AND

y = 1

(then they need disagreement). Averaging the success probability over the 4 equally likely inputs, what is the overall win probability?