Do black holes destroy quantum states?

[Halc]

TL;DR Summary

Article claims thought experiment demonstrates that black holes destroy quantum states.

This pop article popped up (isn't that what they do, by definition?) on my google news page.
https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states

It claims that a thought experiment shows that doing a double-slit experiment near a black hole event horizon can reveal information about its interior, creating a paradox of sorts. This set off all my bells and whistles. Surely I'm not smarter than these guys presenting this scenario at a meeting of the American Physical Society, so I imagine there's a more bonafide description of the paradox, but what I read seems just wrong.

It starts with Alice in a lab orbiting the BH, which is already pretty dang far away. Let's just say she's close. She emits a particle at a pair of slits. It doesn't say where the slits are in relation to the EH, but presumably just outside?? OK so far. We put Bob just inside the event horizon. He can't stay there long, but long enough for this:

When Bob observes which slit Alice’s particle went through, the particle’s quantum state will collapse. That would also let Alice know Bob is there, messing up her experiment. But that’s a paradox — nothing done inside a black hole should affect the outside. By the laws of physics, Bob should not be able to communicate with Alice at all.

That's what set off my alarms. Exactly what does Alice measure that lets her know if Bob did his measurement or not? She just sends photons (or whatever) through the slits and into the BH never to be heard from again. No measurement at all has been taken, and she has no way of distinguishing this quantum collapse from the superposition of which-slit. I see no paradox.

Anyway, is anyone familiar with what actually was argued, and what actual paradox is demonstrated? Theoretically it can be done using a Rindler frame with accelerating Alice somehow determining during acceleration what Bob has done on the far side of the Rindler horizon. After Alice does this, she can stop accelerating and ask Bob what he actually did. Same scenario except we can talk to Bob afterwards.

 

[Nugatory]

Arxiv preprint of the paper: https://arxiv.org/abs/2301.00026

 

[PeterDonis]

Exactly what does Alice measure that lets her know if Bob did his measurement or not?

She can't. There is no measurement Alice can make by herself that will tell her that Bob made his measurement. The only way she can know Bob made a measurement is for Bob to tell her. And of course he can't because he's inside the horizon and she's outside, so he can't send any information to her.

If Wald weren't on the author list of the preprint @Nugatory posted, I would leave it there since the above argument, or something similar to it, appears in many places in the literature. But since Wald is one of the authors, I'm going to assume they actually mean something more subtle that the writer of the Science News article didn't understand (which would not be at all unusual) and read the preprint to see if I can figure out what it is.

 

[PeterDonis]

Arxiv preprint of the paper: https://arxiv.org/abs/2301.00026

It looks like this previous paper is also important, since the present one expands on it:

https://arxiv.org/abs/2205.06279

 

[PeterDonis]

Theoretically it can be done using a Rindler frame with accelerating Alice somehow determining during acceleration what Bob has done on the far side of the Rindler horizon.

The primary analysis is in fact a sort of "Rindler" analysis, but with one key change from what the Science News article (the writer of which, as I suspected, does not actually understand the argument being made) describes: there is no Bob. The horizon plays the role of Bob, but the presence of the horizon, unlike Bob, is not undetectable by experiments Alice can make outside the horizon. That is basically what the paper is describing.

Here is a quick scenario that I believe illustrates the main argument: Alice has a qubit that has been prepared in the z-spin up state. She passes it through a Stern-Gerlach apparatus oriented in the x direction, splitting it into two beams, the x-spin up beam and the x-spin down beam. She then recombines the beams using a second Stern-Gerlach apparatus also oriented in the x-direction, and then measures the z-spin of the qubit. We assume that Alice's lab is perfectly shielded from all non-gravitational influences.

In flat spacetime, the result of Alice's experiment would always be the same: the qubit would be measured at the end to have z-spin up 100% of the time.

However, the paper is arguing that if a black hole is present (or, more generally, if a Killing horizon is present), the result of Alice's experiment will not be to have z-spin up 100% of the time; some of the time, the final measurement will give z-spin down. This indicates a loss of coherence between the two beams while they were separated. The loss of coherence is ultimately due to the presence of the horizon, and Alice's experiment thereby serves as a test for whether or not a horizon is present in her spacetime. Note that the sensitivity of the test varies drastically with altitude above the horizon: the closer to the horizon Alice is, the higher the probability that her final measurement will show z-spin down.