Is attempting to capture the king advisable in this position? This position occurred in a game of quantum chess recently:

 

Is trying to take the king with the queen worth the risk?

My reasoning for this is:


If the bishop is on a2, white can take the king and win the game.
If the bishop is on f7, the queen cannot capture the king, the rook on b1 is safe, and black is able to move the rook on f5 out of danger.


What line would follow if the king capture fails? Would it be more beneficial to ignore the possible check and take the rook on f5? What would the best line be from there?



Confused?

You can check out the rules for Quantum Chess, or read the post written by creator Chris Cantwell.
Interesting!

Based on probability lets say we the bishop being in a2 is equally probable as being in f7 (principle of superposition, quantum chess rules). 

Taking queen with king is blocked if bishop is in f7, which means there is no move occurring in all possible boards. As it is said in the question, rook is moved out of danger. Probability that this occurs is 0.5 and the loss in the game is black becomes stronger than now as the rook is out of danger.

If the bishop is in a2, moving the queen is allowed. White wins, as question states. Probability is again 0.5 and there is no loss for white. 

If the rook is taken instead of moving the queen, again black loses the rook irrespective of where the positioned bishop is. This has a probability of 1. In this situation if bishop is in a2, king is in open check and has to move to g1 or h1, either ways white is way too stronger as it has now 0.5 probability for check mate in consequent step. If the bishop is in f7, king is not in open check and black can play at 50% chance rook b7 as queen can't take rook has 50% and in third move rook takes queen 50% giving 0.125 probability for black to gain hand. 

On conclusion moving queen has 0.5 probability to win the game and 0.5 probability to lose the strong hold and give black more power.

Whereas taking rook has 0.5 probability to win in next move, and less probability that black gains more power.

This is by the way a crude analysis, for just two more consequent steps, as it is quantum chess, anything can happen as the total number of boards increases $2^n$  times for n steps.