If the many worlds of the Many Worlds Interpretation of quantum mechanics are real, there's at least a good chance that Quantum Immortality is real as well: All conscious beings should expect to experience the next moment in at least one Everett branch even if they stop existing in all other branches, and the moment after that in at least one other branch, and so on forever.

Yes, Quantum Immortality is "real", as far as it goes. The problem is that it is inappropriately named and leads to inappropriate conclusions by misusing non-quantum intuitions. So yes, if you plan to put yourself in a 50% quantum death-box and keep doing so indefinitely you can expect there to be a branch in which you remain alive through 100 iterations. The mistake is to consider this intuitively closer to "immortality" rather than "almost entirely dead".

Doesn't it follow that each of us should expect to keep living in this state of constant degradation and suffering for a very, very long time, perhaps forever?

No. Don't do a count on branches, aggregate the amplitude of the branches in question. We should expect to die. There happen to be an infinite (as far as we know) number of progressively more 'improbable' branches in which we are degrading but they still aggregate to something trivial. It is like a zeno's paradox.

I have no idea whether these brief expressions of intuitions that I find useful are at all helpful for you. If not then, like Carl, I recommend this post that explores related concepts with diagrams and examples. (But I'm biased!)

How likely is it that Quantum Torment is real?

The more conventional perspective on QM is of a single nondeterministic world or of a single world in which events have subquantum causes. From this perspective "quantum torment" - lingering indefinitely in a near-death state - is logically possible but inconceivably improbable, something that wouldn't happen even if you reran the history of the cosmos a googol times, because it involves the quantum dice (whether deterministic or nondeterministic) repeatedly coming up just the right way to prevent your body from finally giving up the ghost.

In a many-worlds theory all logical possibilities are supposed to happen, but the empirically validated probabilities still have to be respected. That is, we don't see all possible events occurring with equal probability, we see them occurring with probabilities given by the Born rule of QM. How to justify this within MWI is a major problem, one of several that the theory faces. But assuming that it is resolved, then the frequency with which quantum torment is realized in the multiverse must be the same as the probability with which it is expected in single-world QM, i.e. it represents a vanishingly small fraction of worlds. In the vast, vast majority of worlds you just die.

Doesn't it follow that each of us should expect to keep living in this state of constant degradation and suffering for a very, very long time, perhaps forever?

No. One can't have it both ways. If your consciousness can persist in some infinitesimal state, then one of the things it will have lost on its way to that state is the ability to feel suffering, or boredom, or a sensation of passing time or anything of the like. The ability to feel suffering isn't any more intrinsically a part of us than the ability to see colors or hear sounds.

Besides (though this a rather more far-fetched argument), at the infinitesimal state what is there to meaningfully distinguish your "degraded" dying consciousness from an as-yet-non-upgraded consciousness being born? Instead of Quantum Hell, consider the possibility of Quantum Reincarnation. ;-)

If in one bazillionth of worlds, right now, you are being tortured even though in every other world you are both alive and well, and you don't care about that world because it's only one in a bazillion, there's no reason to care about that one branch more if all the rest of the branches get changed so that you're dead. The amount you care about it should be independent of the amount you care about all the other branches.

The question "Which branch will I go down?" does not specify different ways-the-world-could-be, depending on whether the answer is yes or no. It's meaningless. There is no unique part of you that goes down only one of the branches. Your brain goes down every branch. There is no ghostly essence that is funneled into the branches where you die slowly. Your brain goes into every branch, and in most of them, it dies at the most probable speed.

If the many worlds of the Many Worlds Interpretation of quantum mechanics are real, there's at least a good chance that Quantum Immortality is real as well

Have you read these counterarguments?

If you're prepared to say you're immortal because even if you die you're still alive in some other branch, it seems like you shouldn't even need quantum mechanics. You're immortal because even if you die, you're still alive in the past.

What makes you privilege the experience of dying over other, more positive experiences? That is, even if there's a very large number of branches where we experience this suffering, wouldn't there also be very large numbers of a branches containing positive experiences? It's the ratio of positive to negative experiences that matter, not the raw quantity of one or the other.

ETA: That is to say, the reasoning "when I'm close to dead, no matter how likely I am to die in the next instant, at least one branch of me continues on suffering" is symmetric to "man this hot shower is amazing, good thing there at least one branch of me that continues to enjoy it indefinitely."

Aside from all the other reasons for relief offered in this thread, the fact that you're not in Quantum Hell right now is anthropic evidence that QI isn't true in the sense you should be worried about.

(You may note that this is a generalized argument against most possible forms of immortality.)

All conscious beings should expect to experience the next moment in at least one Everett branch even if they stop existing in all other branches, and the moment after that in at least one other branch, and so on forever.

I don't think this is quite true. Rather, if there is precisely one Everett branch in which a conscious being still exists, they should expect to experience it. If there is no such Everett branch, the conscious being will still be conscious in this moment but will not experience any future moments. If there are multiple, the conscious being should expect to experience one of them.

Since others have already covered the physics side of things:

Your problem here is mostly with using confused notions of things like "conciousness", "real", "expect" and "self". As you level up starts grokking thinking in terms of the measure of computations across the tegmark multiverse and the like, these kind of problems will naturally dissolve. (and be replaced by new arguably much worse unrelated ones)

Quantum immortality as you describe it is not a consequence of MWI. It's not true that every single change in an MWI universe is accompanied by branching. Branching occurs when microscopic quantum superpositions decohere, i.e. when interactions magnify microscopic superpositions into macroscopic superpositions. So branching is the consequence of a particular type of physical process: the "measurement" of a microscopic superposition by its macroscopic environment. Not all physical processes are of this type, and its not at all obvious to me that the sorts of processes usually involved in our deaths are of this sort. When someone gets run over by a bus, for example, what we're dealing with is an already decohered macroscopic system (the bus) interacting with another decohered macroscopic system (the unfortunate victim). We're not dealing with a microscopic superposition getting kicked up to the macroscopic scale. Now it may be the case that the actual processes that go on in the victim's brain after the accident and determine whether she dies or not are "measurement"-type processes, but I'd need to hear an argument that this is usually the case.

Even if one's death can be directly attributed to a measurement-type event, quantum immortality doesn't follow. Say a person gets cancer from a single radiation event (not sure if this is possible, but I'm postulating that it is), and subsequently dies from this cancer. The radiation event is a microscopic quantum process, and his body acts as a macroscopic detector. In this case, one would get branching. One one branch he would get cancer and eventually die from it. On the other he wouldn't get it. But even on the branch in which he dies, death is not instantaneous. He experiences both branches, not just the one in which he lives longer. So this is not a quantum immortality type situation.

One might be able to set up an artificial situation in which quantum immortality is real, but it would have to be a very carefully constructed scenario, one in which the moment of death coincides with the moment of decoherence (of course, neither of these are literal moments). I don't think the circumstances under which most of us die are of this sort.

If you're worried about it, just sign up for cryonics.

In thought experiment (https://en.wikipedia.org/wiki/Quantum_suicide_and_immortality) it says: "Barring life after death, it is not possible for the experimenter to experience having been killed, thus the only possible experience is one of having survived every iteration". QM IMHO does not say about afterlife, so afterlife takes care of Quantum Torment.

I was thinking about this post and thought up the following experiment. Suppose, by some quantum mechanism, Bob has a 50% probability of falling asleep for the next 8 hours and a 50% probability of staying awake for the next 8 hours. By the same logic as QI, should Bob expect (with 100% certainty) to be awake after 2 hours, since he cannot observe himself being asleep? I would say no. But then, doesn't QI fail as a result?