Quantum Tic-Tac-Toe

A Classical Game that Looks Like a Quantum Game

Last month, we asked you to find a quantum game that has no classical game; one solution to that puzzle is given below. This month, we turn the problem around: can you find a classical game that looks like it has to be a quantum game? You get one hint: consider whether the players can do this if they are competing, or if they can only do this by cooperating.

Be sure to include your name and email address! We want to give credit to the person that sends the best solution.

A Quantum Game without a Classical Game

Here's one such game:

Move   X   O 1   2 - 3   3 - 6 3   1 - 5   4 - 7 5   5 - 9   7 - 8 7   9 - 1     9

X wins, no matter how O collapses the cycle formed on move 7. But moves 1, 2, 4 and 6 never collapse, and in the list of classical moves, those moves never happened! What happened to reality? The best way to think about this, is to recall the double-slit experiment. When both slits are open, the only way to explain the interference pattern is to insist that each electron went through both slits. Now, remove the screen where the electrons were detected. Each undetected electron now remains in a superposition; in one classical reality it went through one slit, in the other classical reality it went through the other slit. If you run through the game listed to the left, and look at the Classical Ensemble (tap the Real Games button on the Palm version), you will see nine games in the Classical Ensemble. The quantum reality is OK, it just never collapsed into a single classical reality. Moves 1, 2, 4 and 6 remain in a superposition, but every game in the classical ensemble has the same three X's in squares 1, 5 and 9; the win is not in a superposition, even though all the other moves are. Too way cool.