Each time you press the "Start simulation" button, the simulation of this quantum network including all operations and measurements is run using QuNetSim. QuNetSim is a Python software framework developed by researchers at Technical University of Munich that can be used to simulate quantum networks. The goal of QuNetSim is to make it easier to investigate and test quantum networking protocols over various quantum network configurations and parameters. Learn more about QuNetSim here: QuNetSim: A Software Framework for Quantum Networks
The classical strategy with highest winning probability is given by Alice and Bob setting $(a,b)= (0,0)$ independent of the input $(x,y)$. Doing this, they reach a winning probability of $75%$. $ P(win) = P(a=0, b=0,x=0, y=0)+ P(a=0, b=0,x=1, y=0) +P(a=0, b=0,x=0, y=1) $ $= 1/4 + 1/4 + 1/4 = 3/4 $
$
P(win)= &\sum_{i,j \in \{0,1\}}P(x=i, y=j) P(win|x=i, y=j)
= $
$ \sum_{i,j \in \{0,1\}}\frac{1}{4} P(win|x=i, y=j)
= $ $\frac{1}{4} (P(a=0, b=0|x=0, y=0)+ P(a=1, b=1|x=0, y=0)
+ P(a=0, b=0|x=1, y=0) +P(a=0, b=0|x=0, y=1) $ $
+ P(a=1, b=1|x=1, y=0)+ P(a=1, b=1|x=0, y=0)
+ P(a=0, b=1|x=1, y=1)+ P(a=1, b=0|x=1, y=1)).
$
Alice and Bob's probability to measure $(a,b)$ after applying the rotation $R_Y$ with angles $\theta_x, \phi_y$ based on their inputs $(x,y)$ is given by
$
P(a,b|x,y)= \langle \psi | (R_Y(\theta_x)\otimes R_Y(\tau_y))(P_a\otimes P_b)(R_Y(\theta_x)\otimes R_Y(\phi_y)))| \psi \rangle \\
= \frac{1}{2} |(R_Y(\theta_x)\cdot R_Y(\phi_y)^{-1})_{a,b}|^2
$
where $P_a= \langle a | a \rangle $, $P_b= \langle b | b \rangle $.
The goal of this game is to find $\theta_x, \phi_y$ such that $P(win)$ is maximized.