Thanks for link. I think that communication is impossible when branches are completely separated, but the existence of the trapped ion prevents this complete separation. In other words, the separation has not ended yet in our case and the whole system has to be regarded as one system which evolves linearly.
"Branch separation" is itself contradictory concept as different understanding of what is it exists.
There are different interpretations of MWI, good overview here: https://iep.utm.edu/everett/
For example, if a atom decay, do branches separate everywhere in the universe with superliminal speed? Or branches are separated when we observe different outcomes? See recent discussion Is Branching Truly Global? From Cambridge Changes to Oxford Changes in the Many-Worlds Interpretation
In Plaga model, the trapped ion is isolated from both branches and thus orthogonality equation is not directly applicable to it.
"one does not simply measure whether a system is an eigenstate or a superposition"
We can't do it simply, but with some efforts we can do it. We can measure was the ion in superposition or not if we repeat the experiment many times in exactly the same settings. Eigenstate will give always 1. Superposition state will give mix of 0 and 1 measurements.
The fix is needed mostly not because energy conversation, but because if we transfer any definite state, the sender destroys isolation of the ion by becoming in superposition in it (as was discussed in Quora objection to Plaga model). Here I suggest to use the mere fact of destruction of ion's quantum state as a way to transfer information.
I think it ok to try to patch if costs to check are small and gains if it works are enormous. Any perpetuum mobile developer would say this.
I think that prohibiting is not that strict in the case inter-branch communication when in the case of energy conversation, so adding tricks can work.
Thanks to finding this. As I understood, the rebuttal says that if you excite the ion in one branch, it becomes entangled with that branch and stops being non-entangled with anything. It is easy to see from energy conversation: if I have excited the ion I spent some energy, but if I see the ion excited in another brach, this energy would come from nowhere, which is prohibited by conversation law.
But also I think there still can be way to communicate: I think that instead of exciting ion, the senders have just to measure it (and it should be prepared in a complex state from the beginning). And the receiver will have to measure if ion remains in quantum state or is in one of eigenstates. This makes the whole setup more complex and may require more ions measurements to send just one but of data.
If we take relative states interpretation of Everett (of which MWI is simplification), there is no exact prohibition, but the interference between branches becomes infinitely minuscule very quickly. The only exception is the state of entanglement or any quantum state where a particle has quantum state and didn't yet collapsed to any of eigenvalues.
So the lack of interaction between branches doesn't apply to this experiment because we have trapped ion which still remains in its quantum state.
The problem of the experiment was explained to me in the comment below: If you excite the ion in one branch, it becomes entagled with that branch and stops being non-entagled with anything. It is easy to see from energy conversation: if I have excited the ion I spent some energy, but if I see the ion excited in another brach, this energy would come from nowhere, which is prohibited by conversation law. I think that instead of exciting ion, the senders have just to measure it. And the receiver will have to measure if ion remains in quantum state or is in one of eigenstates.
The problem that you can’t jump anywhere. You can communicate only between two branches which you carefully prepared beforehand - by preparing a ion in a trap and when splitting the branch.
For example, if I did this in the morning today and in the evening one branch has developed misaligned AI and my not (and we have enough trapped ions to send a lot of data) – this mislaigned AI can penetrate my branch. This limitations make risks smaller.
But there can be the ways to bypass this, for example, by finding some natural trapped long-term quantum states (in space? or inside crystals? - Opus said: "Nuclear spins in certain crystals can maintain coherence for remarkably long times—seconds to hours in some cases—because they're somewhat shielded from electromagnetic noise by their electronic environment. Phosphorus-31 nuclear spins in silicon are a famous example. But even these eventually decohere, and they're not truly "trapped" in isolation")
You are correct to point that distributing computation between branches is weakest point here, and in my early draft I wrote that it will not work because slicing computations 2 times between two branches is not a major gain and 1-bit channel is very thin information channel to transfer useful information about the results of computations. However, I changes my mind when I start imagine more complex constructions with multiple ions and forks.
If the branch-communication is real, advanced mind will find the ways to use it to accelerate some types of compositions.
I think the more use - if it will work - will come not from accelerating computations but from measuring some real world data in other branch. James Miller commented to the draft:
"This would have massive value. Imagine I need a dangerous operation.
It is done in one branch of the multiverse, and results are
communicated to the other before other decides if they should do it as
well. Or with computing. A branch spends 20 minutes doing some
computation and then tells the other branch if the computation was
worth doing. On a simpler level, you ask a girl on a date and report
if she said yes or no to yourself in another branch so he doesn't have
to risk rejection."
If you argue that branch communication is not real, there should be a reason: either MWI is false or in this exact setup there is some technical or theoretical flaw. As I think you are pro-MWI and there is not much technical details, there should be some theoretical problem. What it could be?
Or you argument can be interpreted socially: people are spending billions on quantum computers but did not ever tried an experiment which will cost much less then 1 million despite that they can earn hundred billions of dollars if it works (mostly via high-frequency trading). As there is no free money laying on the road, there must be obvious flaw. I am also puzzled about this.
It is similar idea but it requires quantum computer. and only provide computation results. Deutsch also suggested testing MWI via some quantum computer setup. The closes idea is quantum bomb tester - and such tester can be used for inter-branch communications if we turn off the bomb in the worlds where we want to send 0.
The main difference is that here we can send real world macro data like trade results or even movies to another branch.
S.Aaronson wrote that quantum computing is not distributing of computations between branches and inter-branch communication is not quantum computing, so I am not sure that comparing with quantum computing helps.
Anyway, there is a restriction in this setup: the communication can happen only between two branches.
However, one of the branches can be branched again during the experiment and return information to second branch which will later return it to first branch. Thus we can exponentially increase the number of different branches with we are communicating though this is not all branches. This gives us exponential increase of the complexity of tasks which can be solved but the price will accumulate quickly as each forking and return of information should be shorter in time.
I understood your idea. From early Plaga point of view the branches are in the process of separation, so they are not yet real branches and this allows short period of communication. I would be interested to see experimental test.