# Anton Potočnik

at imec

# Qballs

During my ski trip I got an interesting idea about a simple arcade game with a completely different approach. In this game the player has to find entangled balls.

### Game instructions in English

Each ball in the game has two possible colors that are randomly changing. Entangled balls have always connected colors. This means that if the color of one ball changes, all that are entangled to it must change their colors instantly. There are two possible entangements: one is symmetric, where all entangled balls have the same color, and the other is antisymmetric, where colors of entangled balls are always different. If, for example, two balls have at first the same and later the opposite colors, they are not entangled! Usually, you have to search for pairs of entangled balls, however, at some levels you have to find triples. In this case antisymmetrically entangled balls have two with the same color and the third with a different color.
When you think you found the entangled balls select them with a mouse click. If the selected balls are not entangled, the elapsed time will increase for 5 penalty seconds!

### Navodila v Slovenščini

Vsaka žoga v igri ima lahko dve različni barvi, ki se naključno spreminjata. Igralec išče žogice, ki so med seboj prepletene (entangled), kar pomeni, da če se eni žogici spremeni barva se mora hkrati spremeniti barva tudi vsem, ki so z njo prepletene. Žogice so lahko prepletene na dva načina: v prvem simetričnem (symmetric) načinu imajo prepletene žogice vedno enako barvo, v drugem, antisimetričnem (antisymmetric) pa imajo kroglice vedno različno barvo. Če imata dve žogici nekaj časa enako in nekaj časa različno barvo, potem ti dve nista prepleteni. Pogosto prepletene žogice nastopajo v parih, le pri nekaterih stopnjah pa tudi v trisih. V tem primeru za antisimetrične trise velja, da imata dve žogici enako barvo, tretja pa drugačno.
Prepletene kroglice se išče tako, da na njih klikneš z miško in jih označiš. Če označene kroglice niso prepletene dobiš dodatnih kazenskih 5s pri prištevanju časa.
Qballs
Choose the level and press Start button!

 Level 1: 2×2 2sPLevel 2: 2×2 1aPLevel 3: 3×3 4sPLevel 4: 3×3 4aPLevel 5: 3×3 1sP Level 6: 3×3 1aPLevel 7: 3×3 3sTLevel 8: 3×3 3aTLevel 9: 3×3 1sTLevel 10: 3×3 1aTLevel 11: 4×4 8sPLevel 12: 4×4 8aPLevel 13: 4×4 1sPLevel 14: 4×4 1aPLevel 15: 4×4 5sTLevel 16: 4×4 5aTLevel 17: 4×4 1sTLevel 18: 4×4 1aTLevel 19: 5×5 12sPLevel 20: 5×5 12aPLevel 21: 5×5 1sPLevel 22: 5×5 1aP

Wavefunction of the entangled particels:

Is this game related to quantum mechanics? Yes! The two colors represent two quantum states. If a particle has two states with equal energy, a measurement of it’s state will randomly result in one or the other state with equal probability. An example of such a particle is an electron with a spin S=1/2 pointing up or down.
In quantum mechanics particles can interact and become entangled. Two entangled particles are connected in such a way that as soon as one particle’s state is measured the state of the other particle is immediately determined. Depending on the symmetry of the entangled particles the second particle will always be in the same or the opposite state with respect to the first particle.

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