The Quantum Tris (in English Quantum Tic Tac Toe) is a version of Tris in which each The uncertainty of the positions of the X and O particles makes it difficult to predict what will happen in the following rounds and the games take place in a compelling mix of physics and strategy. Let’s see what the rules of the game are and what these have to do with the concepts of entanglement, superposition and state, characteristic of quantum physics.
The rules of Quantum Tris
The competition field is identical to that of classic trioa table of nine boxes (3×3) to be filled in turn with the particles of the game (the X and O signs) with a special move called quantum move. Let’s see how to proceed in detail, starting from quantum move, according to which
two squares are occupied at a time: at each turn the player occupies temporarily two boxes of your choice with your own sign (X or O) and connect with a line (which we call entanglement) the two signs drawn.
In practice the player reserves two spacesbut at the end of the game he will only be able to occupy one. In the figure below (on the left) the first player has occupied the top left and central square with the X and has connected the two entanglement. At the end of the game the X in question can only be in one of the two boxes, either the top left one or the central one.
One box can temporarily accommodate multiple signsbut only one of them will remain there until the end of the game.
In the figure above (on the right) after 4 turns, the central square is booked by two X-type particles and one O-type particle, but only one of the three will be able to definitively occupy the square. This situation of indeterminacy is resolved when a cycle of connections is created, a cycle of entanglement (see figure below).
When a player completes an entanglement cycle the particles that compose it collapse and each particle in the cycle must occupy only one position, as if it were a normal X (or O) of the classic three of a kind.
Since there are two positions reserved for each particle, a cycle can be solved in two different ways. To do this, you just need to decide the final position of just one particle of the cycle itself and the positions of the other particles will be determined accordingly. For example, in the figure below if you decide that the On the right of the figure we see what happens if we instead choose for the X to occupy the box at the bottom left.
But who decides how the cycle is resolved? The rules of the game state that
When a player completes a cycle, the opposing player decides in which of the two ways to solve the cycle.
Once solved a loop, the particles who were part of it they each occupy their own spaceas in the classic trio. In our example, see figure below, we have solved the loop in one of two possible ways, but the central box still hosts an X that was unrelated to the loop and which is connected to the X of the top left box.
This situation is resolved with the rule according to which
A space permanently occupied by an X or an O cannot host other particlesany other particles found in the box will be forced to occupy the entangled box.
In the right part of the figure above you can see how the game board appears after the cycle has been resolved. At this point the players can continue to occupy pairs of squares, choosing from those not permanently occupied, and resolving any new cycles that will form, according to the rules we have stated.
The game ends when one of the two players achieves a three of a kind or when it is no longer possible to do so quantum moves as all the boxes (or all but one!) are permanently occupied. However, unlike the classic three of a kind, it may happen that a player achieves more than one three of a kind, or even that both players achieve at least one three of a kind, in which case there will not be a draw, but there will be two winners.
This game was created in 2002 by Alan Goffof theAmerican Institute of Aeronautics and Astronauticswith the intention of providing a metaphor for some aspects of quantum physics, among these aspects we mention two. The first is the analogy between the entanglement of quantum physics and the bond, which we have called proper entanglementbetween the two positions initially occupied by each particle in the course of the game. A second aspect that we can consider is the state of uncertainty of the position of a particle in the game, which we can trace back for example to cases such as that of Schroedinger’s Cat whose state remains uncertain until a measurement, an observation, occurs, which in the case of the game corresponds to the moment in which a cycle is completed and resolved.
