Marro quàntic

Fa pocs dies que vaig conèixer per casualitat una versió diferent del “marro” o del “tres en ratlla”, tot buscant jocs de caire quàntic. A la wikipedia s’hi descriu el joc Quantum Tic Tac Toe, on el smoviemnts són força més complexos que no pas el marro normal (o les seves moltes variants popularitzdes per en Martin Garder), i demanen tenir un cert coneixement de mecànica quàntica, del concepte d’entrellaçament, i el concepte fonamental de mesura. I natualment el de col.lapse de la funció d’ona.

De fet, he instal.lat una aplicació al meu Iphone (via Apple Store) que permet jugar al Marro Quàntic. Espero poder dominar aviat (en un temps imaginari?) la maquineta.

M’agradarà en el futur conèixer altres jocs per explicar, si pot ser de forma planera, la mecànica quàntica.

Les regles d’aquest joc, ben explicades a la wikipedia, són

Quantum tic-tac-toe captures the three quantum phenomena discussed above by modifying one basic rule of classical tic-tac-toe: the number of marks allowed in each square. Additional rules specify when and how a set of marks “collapses” into classical moves.

On each move, the current player marks two squares with their letter (X or O), instead of one. The pair of marks are called spooky marks and are subscripted with the number of the move. (For example, player 1’s first move might be to place “X1” in both the upper left and lower right squares. Because X always moves first, the subscripts on X are always odd and the subscripts on O are always even.) The two squares thus marked are calledentangled. During the game, there may be as many as eight spooky marks in a single square (if the square is entangled with all eight other squares).

The phenomenon of collapse is captured by specifying that a “cyclic entanglement” causes a “measurement”. Acyclic entanglement is a cycle in the entanglement graph; for example, if square 1 is entangled via move X1 with square 4, which is entangled via move X3 with square 8, which is in turn entangled via move O4 with square 1, then these three squares form a cyclic entanglement. At the end of the turn on which the cyclic entanglement was created, the player whose turn it is not — that is, the player who did not create the cycle — chooses one of two ways to “measure” the cycle and thus cause all the entangled squares to “collapse” into classical tic-tac-toe moves. In the preceding example, since player 2 created the cycle, player 1 decides how to “measure” it. Player 1’s two options are:

  1. X1 collapses into square 1. This forces O4 to collapse into square 8 and X3 to collapse into square 4.
  2. X1 collapses into square 4. This forces X3 to collapse into square 8 and O4 to collapse into square 1.

Any other chains of entanglements hanging off the cycle would also collapse at this time; for example, if square 1 were also entangled via O2 with square 5, then either measurement above would force O2 to collapse into square 5. (Note that it is impossible for two or more cyclic entanglements to be created in a single turn.)

When a move collapses into a single square, that square is permanently marked (in larger print) with the letter and subscript of the collapsed move — a classical mark. A square containing a classical mark is fixed for the rest of the game; no more spooky marks may be placed in it.

The first player to achieve a tic-tac-toe (three in a row horizontally, vertically, or diagonally) consisting entirely ofclassical marks is declared the winner. Since it is possible for a single measurement to collapse the entire board and give classical tic-tac-toes to both players simultaneously, the rules declare that the player whose tic-tac-toe has the lower maximum subscript earns one point, and the player whose tic-tac-toe has the higher maximum subscript earns only one-half point.