The quantum Russian roulette is a game where 16 people participate. Each of them gets a unique four digit binary code assigned and deposits $50000. They are put to deep sleep using some drug. The organizer flips a quantum coin four times. Unlike in Russian roulette, here only the participant survives whose code was flipped. The others are executed in a completely painless manner. The survivor takes all the money.
Let us assume that none of them have families or very good friends. Then the only result of the game is that the guy who wins will enjoy a much better quality of life. The others die in his Everett branch, but they live on in others. So everybody's only subjective experience will be that he went into a room and woke up $750000 richer.
Being extremely spooky to our human intuition, there are hardly any trivial objective reasons to oppose this game under the following assumptions:
- Average utilitarianism
- Near 100% confidence in the Multiple World nature of our universe
- It is possible to kill someone without invoking any negative experiences.
The natural question arises whether it could be somehow checked that the method really works, especially that the Multiple World Hypothesis is correct. At first sight, it looks impossible to convince anybody besides the participant who survived the game.
However there is a way to convince a lot of people in a few Everett branches: You make a one-time big announcement in the Internet, TV etc. and say that there is a well tested quantum coin-flipper, examined by a community consisting of the most honest and trusted members of the society. You take some random 20 bit number and say that you will flip the equipment 20 times and if the outcome is the same as the predetermined number, then you will take it as a one to million evidence that the Multiple World theory works as expected. Of course, only people in the right branch will be convinced. Nevertheless, they could be convinced enough to make serious thoughts about the viability of quantum Russian roulette type games.
My question is: What are the possible moral or logical reasons not to play such games? Both from individual or societal standpoints.
[EDIT] A Simpler version (single player version of the experiment): The single player generates lottery numbers by flipping quantum coins. Sets up an equipment that kills him in sleep if the generated numbers don't coincide with his. In this way, he can guarantee waking up as a lottery millionaire.
Why is that? In order for function minimization to be in NP, you have to be to write a polytime-checkable proof of the fact that some input is a minimum. I don't think that's true in general.
I also don't see how function minimization can be accomplished using quantum suicide. You can compute the value of the function on every possible input in parallel, but how do you know that your branch hasn't found the minimum and therefore should commit suicide?
This seems like a relevant article, although it doesn't directly address the above questions.
ETA: I do see a solution now how to do function minimization using quantum suicide: Guess a random x, compute f(x), then flip a quantum coin n*f(x) times, and commit suicide unless all of them come out heads. Now the branch that found the minimum f(x) will have a measure at least 2^n times greater than any other branch.
ETA 2: No, that's not quite right, since flipping a quantum coin n*f(x) times takes time proportional to f(x) which could be exponential. So I still don't know how to do this.
...That's an interesting way to look at it. For example take the traveling salesman problem: it's traditionally converted to a decision problem by asking if there's a route cheaper than X. Note that only "yes" answers have to have quickly checkable certificates - this is NP, not NP intersected with co-NP. Now if we start asking if X is exactly the minimum ... (read more)