What matters is that all these transformations are unitary, so they are in principle allowed in quantum mechanics.

]]>She must do this after making her quantum measurement, therefore she will be in a superposition, and two copies of her will be sending the qubit which must be received as a single qubit.

That qubit, according to the procedure laid out by Renner and Frauchinger, must have the state “down” for one of the copies of Fbar, and the mixed state “up + down” for the other Fbar.

Is it impossible, as you just said, for these two copies of the qubit to “recombine” ?

The experiment also requires that both labs be measured in the basis ” ok – fail ” when the setup is complete. This is not their natural basis.

I therefore suggest that they would need to emit a qubit, in much the same way as above, so that their state could be measured in some other basis than the natural one.

But, encoding their state would once again require that each copy of the superposed agent put the qubit into a different state.

Is “recombination” impossible here too? Can this whole experiment exist, in principle?

]]>When last I wrote, I was worried about the qubit that goes from /L to L.

I thought that both copies of it (from the two superposed copies of the lab) would need to “decohere” into a single copy, such that if you got a “down” reading in lab L, you would be unable (in principle) to know the state of lab /L.

I can see now that’s not necessary.

It’s not necessary to “recohere” the qubits from the two superposed copies of /L. It doesn’t matter if they are incoherent. It doesn’t matter if lab L is fully aware of the state of lab /L. The overall system will still end up in the desired configuration (three states with 1/3 probability each).

So, your proposed mechanism of controlled wave plates, is not necessary for the qubit S.

But I’m also worried about the final measurements made by W and /W.

You see, the experiment requires these external agents to measure the labs in a basis called “ok / fail “.

This is not the natural basis of the lab contents. With this basis, the agents are in superposition after measurement! This basis cannot possibly be used by somebody opening the lab and examining its contents; instead, the lab must somehow send its state out, encoded into something, for measurement.

Now, I’m looking at your proposed mechanism of controlled wave plates. Can it be used in this situation? Can an agent, within a lab, encode her state into a photon by polarising it, such that the two superposed copies of the photon (from two superposed copies of the agent) will combine into a single photon?

Once again, I see a possible violation of the No Cloning Theorem, but I don’t understand it well enough to wield it here, so let’s ignore that.

Because I see another problem.

For the two copies of the photon to recombine, is interference. Their wave functions would add.

But we’ve just given them orthogonal polarities. Doesn’t that preclude them interfering as we want?

]]>So, my concerns about the quantum state being measured twice are not relevant. ]]>

Now, the delicate thing is, that in general one would entangle more degrees of freedom with the result of the measurement than just the polarisation (for example, the time of emission, as you mentioned). If this happened the state of the photon would become maximally entangled with the state of $\bar{\text{F}}$, and this would ruin the experiment. But there is nothing fundamental about this. One can synchronize very well the time of emission (for example by doing it before the measurement), and take care that nothing changes in the photon except the polarisation. Yes, it is difficult, but this *gedankenexperiment* is not about what is easy, but what is in principle possible.

My point is that “S” physically leaves laboratory /L and travels to laboratory L, in order to entangle L with the quantum state of the “coin”.

I’m not assuming that “S” is an electronic device containing a qubit. It could be something as simple as a photon. But it must physically exit from /L and travel to L.

So, there will exist something (probably a photon) outside of lab /L, bearing a quantum state that originated in the “coin”.

And we ALSO need agent /F to read the “coin” so that she, and her lab, will go into a superposition.

How would you implement this?

]]>>> “the argument asks … to transform… (some stuff) into (other stuff) which is just a controlled Hadamard”

All right, so let’s build a quantum pathway inside lab /L, as follows :

“coin” -> Hadamard circuit -> output

Now, correct me if I’m wrong. I think there should be no “measurement” anywhere along this quantum path. Otherwise, the state would “collapse” and the output would be altered.

Therefore, agent /F, her table, her chair and her coffee…. will not enter the superposition state.

Am I wrong there?

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