The website for this game can be found at http://www.paradigmpuzzles.com/
The simplest discussion of the game is the four-page document – for teachers. Under downloads you can also find a 22 page document, of which the first 14 pages are about tic-tac-toe.
Whydon't you can skip all that, and just play the game. All you really need are the rules but if you use the Play function, it helps you keep track of the rules and displays all the classical games that might result from this quantum game.
This game illustrates many key features that are common to quantum systems.
1) The moves are indeterminate. Instead of placing an ‘x’
in a given square, you give it a probability to be in two different
squares, so it is in a superposition of discrete states.
2) The quantum moves may entangle by sharing squares. If X1
and X3 and O2, all have a probability to be in a given square, then their fates
are connected or entangled. If X1 is measured to be in that square, then X3
and O2 can’t be there, and are therefore definitely found in their other
possible squares. This entanglement gives a sense of how quantum computing works.
Furthermore, a classical computer can easily handle classical Tic-Tac-Toe but
will have problems with this quantum version - especially if you go to larger
boards. A quantum computer will not have this problem.
3) Eventually, there will be a cyclic or self-referential entanglement. This
entanglement means that there are now only two possible self-consistent classical
results. No more possibilities can fit into the cyclically entangled squares
without causing a paradox. In the game, the next player chooses which outcome
happens. A more realistic version would have you flip a coin, but it wouldn’t
be as much fun to play. There wuld be too much chance and too little skill.
In the real world this collapse of the possibilities occurs when a measurement
is made. Measurement affects the final result of a quantum system and we always
find the quantum object in a specific discrete state.
4) When the states collapse in this game, you can get results that would not
occur in a classical game because more than one move appears at once. There
isn’t a linear progression in time of one move after another, with a clear
path of cause and effect. You can have both players win or even the same player
win twice! This instantaneous collapse appears to violate relativity or local
reality and is the basis of the EPR ‘paradox’. This is like what
nature does, whether we think it makes sense or not. Even without such obvious
differences the final boards do not look like boards played by classical rules.
They don’t call for any illegal moves - just incredibly stupid moves.
For example, suppose the board has x winning on her third turn. Why wasn’t
the third square taken by O on his second turn?