This question is about the Magic Squares game. Links here, here and link here in which two players try to win a game. It's a cooperative game - either the team wins or the team loses. It is claimed that without a shared quantum state, they lose at least 1/9 of the time. The rules of the game are as follows: There is a 3 by 3 grid, and Alice lays down zeros and/or ones on one of the rows. Bob lays down zeros and ones on one of the columns. The referee tells Alice what row to put her digits in and tells Bob what column to put his digits in.
Alice's row has to have an even number of ones and BOb's column has to have an odd number of ones.
There is one square in common between Alice's row and Bob's column. In order to win, Alice's digit there has to match Bob's digit there. If they are different, the players lose.
The question is: can Alice and Bob use a shared quantum state prepared before the game starts to win 100% of the time and, if so, what measurements and quantum operations do they perform?