2. Superpositions
In quantum chess, pieces can occupy superpositions of squares. On the quantum chessboard below, the white queen is on D1 and F5 at the same time
There isn't a complicated explanation which would make things clear :)
Superpositions simply exist. Their existence is one of the fundamental laws of nature. Our world is like that.
In everyday life we don't see superpositions much, because they tend to quickly get evaporated because of the violent interactions with the environment. But in principle, you can preserve superpositions and work with them! That's what they are trying to do in order to get the quantum computer working.
How would we, as human being, perceive quantum superpositions? Well, until we do, there couldn't be a clear answer :)
What we do know already is how our equipment (measuring devices like microscopes) perceive superpositions. From this we have experimental evidence that the existence of superpositions does influence the system.
Well, we can adjust two kinds of interpretations:
- We can say, as we did before, that the white queen is on two squares simultaneously. That would be true, but it is hardly a satisfactory explanation.
- We can say that the white queen is either on D1 or on F5 – we just don't know yet. This isn't correct in all cases, meaning that until the exact position of the white queen is decided, both positions play a significant part in the development of the game. The position of the white queen is not predetermined.
But this second interpretation offers a beautiful insight on how superpositions behave in some situations. Sometimes a specific situation arises in the game, when the quantum chessboard can no longer exist in superposition consistently. Whenever this happens, a measurement occurs.
Measurements assign positions to some quantum pieces, following the rules of the game described in this document. The choice is always made randomly, based on the probability, which is shown for each piece by the special probability-meter.
For example, on the quantum chessboard above the white queen has a 50% chance of revealing itself on either D1 or F5 upon measurement. However until it happens, it will happily sustain itself in the quantum superposition.
Again: the probabilistic interpretation is only correct when the measurement happens. Besides measurements, quantum superpositions exist on their own.
Suppose that on the quantum chessboard above, the blacks decide to play black bishop C8 : F5 takes queen. Will this trigger a measurement to decide whether the queen is captured or not?
No. The amount of inconsistency caused by this move isn't enough to destroy the quantum superposition (the exact criteria of which can be found below in this document).
Instead, bishop will capture half queen:
The white queen is now in the quantum superposition of being dead and alive, just like Schrodinger's cat! The game goes on, leaving whites in frustration of whether they have a queen or not. Just like with any superposition, of course, the fate of this issue is undetermined at this point. Whenever the measurement will occur, whites will find themselves in possession of the queen with 50% chance :)