3. Measurements
Measurements, as was mentioned earlier, assign positions to superposed pieces. What needs to happen in order for measurement to occur? We have a pretty well-formed criterion of this:
Whenever any square of the chessboard appears in a superposition of being occupied by different pieces (belonging to the same player, or to different players), a measurement occurs in order to determine which piece occupies the board. Measurements are designed to be of minimal influence on the existing superposition. They will only resolve conflicts between pieces for any square of the chessboard, leaving untouched any superposition which doesn't pose such conflicts.
For example, say whites decide to have their revenge on the black bishop on F5. They play white queen D1 F3 which doesn't trigger a measurement, of course, but only moves half-queen to F3. The blacks play black pawn A7 A6 and whites decide to take a stab: white queen F3 : F4 takes bishop.
Before the final move, the board looks like this:
Now comes the interesting part. The square F5 appears to be shared by a superposition of pieces: the white queen and the black bishop. We know from the criterion above that this isn't allowed. A measurement will be triggered by the quantum chess engine in order to randomly assign the piece to the square F5. There could be two equal-chance possibilities here.
The first is: the capture succeeds. In this case the queen is no longer dead-and-alive: it would be unfair to the whites to require them to take a 50% chance each time their queen makes a capture. Once something is decided by the measurement it becomes true. In this case, the white queen is put into existence by measurement:
The second is: the capture fails, revealing that the whites don't have a queen. It isn't correct to say that they didn't have a queen all along, though. The measurement has just happened, it decided that the queen is already captured just now. In this case the board looks like this:
Captures with superposed pieces aren't the only example of a situation where a conflict occurs and triggers measurement.
Another common way to measure superpositions is by making a move on the superposed square. Say for example that whites are uncomfortable with playing half a queen. They want the existence of their queen to be decided momentarily. Luckily, there's a move which accomplishes this: white king E1 D1.
After this move, D1 is in superposition: it is simultaneously occupied by the white queen (which was there from the start, in this case the move with the king failed) and by the white king (this can only happen if there's no queen at D1, in this case the move with the king succeeded). As we can see, this move measures the position of the white queen!
The two possible outcomes are:
Note that in the first case the queen is determined to exist, and the white king hasn't moved at all. The whites have spent their turn to act on measuring the superposition.
In the second case, the white queen is rendered dead. The white king has moved to D1.