A Quantum Game

Bell came up with “nonlocal” games, which require players to be at a distance from each other with no way to communicate. Each player answers a question. The players win or lose based on the compatibility of their answers.

One such game is the magic square game. There are two players, Alice and Bob, each with a 3-by-3 grid. A referee tells Alice to fill out one particular row in the grid — say the second row — by putting either a 1 or a 0 in each box, such that the sum of the numbers in that row is odd. The referee tells Bob to fill out one column in the grid — say the first column — by putting either a 1 or a 0 in each box, such that the sum of the numbers in that column is even. Alice and Bob win the game if Alice’s numbers give an odd sum, Bob’s give an even sum, and — most important — they’ve each written down the same number in the one square where their row and column intersect.

Here’s the catch: Alice and Bob don’t know which row or column the other has been asked to fill out. “It’s a game that would be trivial for the two players if they could communicate,” said Richard Cleve, who studies quantum computing at the University of Waterloo. “But the fact that Alice doesn’t know what question Bob was asked and vice versa means it’s a little tricky.”