While Schrödinger’s cat illustrates superposition, it may trigger some simple questions
- When we physically open the box, there is a 50% chance of seeing the cat either live or dead (clearly not both). So what does it even mean to say the cat is both live and dead when we haven’t looked inside, apart from the question evoking memory of equivalently vacuous babble on the same topic about trees falling in forests and not being heard etc?
- Even if we grant the cat is both live and dead before we open the box, what can we do with the information that the “cat is both live and dead”?
The following game will show how we can increase the odds of winning from 50% with a regular fair coin to 100% with a “quantum coin” by
- leveraging off information equivalent to “both live and dead cat state”, that is the quantum coin “in both heads and tails state” — and just a little cheating.
- The best part is even if our cheating is exposed by our opponent, the cheating will seem like an insignificant detail.
- Neither us or our opponent (or anyone else in the world for that matter) will have any satisfying common sense explanation for why we can always win, despite knowing how we can win when we cheated.
Regular coin game.
Lets first do the game with a regular fair coin.
- We place coin in a box.
- We declare our choice to our opponent — say heads.
- We shake the box and let the coin settle.
- We can choose to open box at this step and see if its heads or tails at this point, but it doesn’t matter — the rules of the game says we have to shake the box again one more time and let the coin settle.
- We now open the box to see if we won or not.
It is obvious that our chances of winning is 50%. Also, it doesn’t really matter if we opened the box and looked inside at step 4. If we played this game, say a 1000 times, regardless of us looking at the intermediate result at step 4, the chance of winning is always 50%. Figure 1 illustrates this.