I think I have got it: Re: Scott Aaronson: It’s hard to think when someone Hadamards your brain: Frauchiger and Renner say: State |ψ>:

$|\psi> = \frac{|00> + |01> + |10>}{\sqrt{3}}$

and Alice and Bob will measure the first and second qubits of this state in the basis {+,-}. There are three components to the state |ψ>, and in them:

1. |00>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>. If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.
2. |01>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>.
3. |10>: If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.

Frauchiger and Renner then say: Turn these counterfactual subjunctive "were to measure in {0,1}"s into actual measurements by having Charlie and Dianne do their own measurements in the {0,1} basis on the first and second qubits, branching the universe into (1), (2), and (3).

1. In this branch Charlie knows that Bob will measure |+> were he to get around to measuring before decoherence of the second qubit takes place, and Dianne knows that Alice will measure |+> were she to get around to measuring before decoherence of the first qubit takes place.
2. In this branch Charlie knows that Bob will measure |+> were he to get around to measuring before decoherence of the second qubit takes place.
3. In this branch Dianne knows that Alice will measure |+> were she to get around to measuring before decoherence of the first qubit takes place.

Frauchiger and Renner then say: In each branch, Charlie and Dianne write down, respectively, "I have measured qubit 1 in the {0,1} basis, and I may know that Bob will measure |+>" and "I have measured qubit 2 in the {0,1} basis, and I may know that Alice will measure |+>". They then apply the fact that Charlie and Dianne have measured and the principle of the excluded middle to conclude that it is logically impossible—no matter how the branching has taken place—for both Alice and Bob to simultaneously measure |-->.

Frauchiger and Renner then say: If we then opened the boxes and decohered Charlie and Dianne, we would be done. But...

Frauchiger and Renner then say: Frauchiger and Renner then apply quantum erasers to Charlie and Dianne. The quantum eraser leaves their "I have measured..." messages intact and visible. But the quantum erasers recombines the branches and the restored coherent state is still (or again?) |ψ>. And then when Alice and Bob do their measurements in the {+,-} basis, 1/12 of the time we find |-->. And so either the principle of the excluded middle or the standard use of the subjunctive must fail for QM to be true.

But actually: State |ψ>, and Alice and Bob will measure the first and second qubits of this state in the basis {+,-}…

There are three components to the state |ψ>, and in them:

1. |00>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>. If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.

2. |01>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>.

3. |10>: If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.

Frauchiger and Renner then turn these counterfactual subjunctive “were to measure in {0,1}”s into actual measurements by having Charlie and Dianne do their own measurements in the {0,1} basis on the first and second qubits, branching the universe into (1), (2), and (3).

But, contrary to Frauchiger and Renner's reasoning above, actually:

1. In this branch Charlie knows that if the wave function has collapsed—if the universe has branched—Bob would measure |+> were he to get around to measuring before decoherence of the second qubit takes place. In this branch Dianne knows that if the wave function has collapsed—if the universe has branched—Alice would measure |+> were she to get around to measuring before decoherence of the first qubit takes place.

But Charle and Dianne know that even though they have done their measurements they are in their boxes, and hence the wave function has not yet collapsed—the universe has not yet branched.

Thus Charlie and Dianne know that when it comes time for Bob and Alice to do their measurements in {+,1}, there will be contributions not just from the $\frac{|00>}{\sqrt{3}}$ component of $|\psi>$, but from the $\frac{|01>}{\sqrt{3}}$ and the $\frac{|10>}{\sqrt{3}}$ components of $|\psi>$ as well.

And so they do not know that if Bob were to measure in {+,-} Bob would measure |+> and that if Alice were to measure in {+,-} Alice would measure |+>.

Instead, they know that they are uncertain about what Bob and Alice will measure. They know that the facts that Charlie and Dianne know that they have obtained definite results in the {0,1} basis have (or will have had) no consequences for the true wave function, which remains the original $|\psi>$, and will remain $|\psi>$ until Alice and Bob do their measurements.

2. Similar...

3. Similar...

?

And is the lesson that:

(A) Many-worlds does not have a problem if agents properly understand what the branching structure of the universe will be when decoherence occurs.

(B) Other approaches have a big problem, because not even conscious and certain measurement by Turing-Class intelligences justifies a movement from the quantum-superposition to the classical-probabilities level of analysis.

?