Strategic

 In the IBM Quantum version of the CHSH game, Alice and Bob still each return

0 or 1, but do so after measurement. Here is the strategy each follows:

Alice:                                                    

Bob:

                                                                                    

Effectively, each has created an orthonormal basis of 90 degrees.

                                                             

How does this better their chances. Below, for the case where each receives

a 0 from the referee:

                                                                                         

        
 Overall probabilities:

                                                                              

Doing the math, this means that a = b app. 85% of the time., a net improvement 

from a classical strategy.

There is Qiskit code for running the game with this strategy, which I plan to

work on next!! 🎲

This is the end of IBMLearn quantum info. I did try to drawTHE ciecuit for all

these possibilities, but then realized that there is not one circuit but four and each

is run as a function of what the referee assigns to Bob and Alice. From the qiskit 

implementation in the lesson:

                                              

My run won .86 out of 1; and my classical run.754.

                                                                      *     *     *

Quirk has its own version:

                                                                                  

Noteworthy that the referee gets a Hadamar gate which is measured...