Testing Black Hole Information With Entangled Particles

If we create a pair of entangled photons, shoot one inside a black hole and then measure the spin of its safely hidden companion, we would then know information inside a black hole. Doesn't it settle down the issue wether or not information is destroyed inside a black hole?
- Anonymous

Hi Mr. Anonymous,

That's a fantastic question... or at least I think so, since it is one of the first questions which lured me into studying quantum mechanics. Unfortunately, the idea doesn't work, and here's why. Short version: to get any information out of an entangled pair of particles, you have to look at and do measurements on both particles. Unfortunately, one is irreversibly in a black hole, so you can't do that.

Slightly longer version: this answer is identical to the reason why you can't send signals faster than light using quantum entanglement, or why delayed choice quantum erasers don't change the past. In all cases, you start with an entangled pair of particles, send one off to a distant point, perform measurements on your particle, and see what you learn. It turns out, from your particle alone, you don't learn anything at all! Assuming you started with a perfect (maximally) entangled state, then your measurement result will be completely random. 

The weirdness of quantum entanglement only shows up if you look at the second particle of the pair as well. Usually this is done by a distant observer, who also gets a totally random result. Yet somehow, if he meets up with you later and you compare results, you will find that any time you measure the same property of the particle, you get the same result! The outcomes are totally random, but totally correlated. You only see the correlation if you check both particles.

So, if you throw one particle into a black hole, you simply lose all your information about it, and your own particle looks totally random (aka a "mixed" state). If you want a bit more explicit explanation (which doesn't involve black holes, but has the exact same point), then check out this question: 

Hope that helps,

David Schmid

But there is another level of complication. We think that black holes aren't really permanent. They will ultimately evaporate via Hawking radiation. In fact, since the black hole never quite forms (from the perspective of a remote observer), an almost-black-hole should evaporate by almost-Hawking-radiation, staying within the framework of quantum field theory. So that other spin may not be really lost. Thisissue is related to the black hole firewall paradox that has been the subject of much discussion recently. ()

Mike W.

(published on 06/26/2014)