> I thought you were referring to the relativity of simultaneity.

Yes, I was.

> I'm glad you insist on the FTL communication issue,

It amounts to the same thing.

> maybe now I will be able to convince you that there is no issue at all...

Maybe, except that I'm not sure you're clear on what we're actually disagreeing about.

> You say that, before any message from Alice can reach Bob, he can determine wheter or not she has performed the measurement.

Only in a hypothetical case, not realizable in practice (probably -- see below), where Bob has chosen N/4 particles at random and those just happen to coincide with the particles that Alice measured and found to require no rotation. In that case, Bob will, on your view, observe first-order interference if Alice has measured, and not otherwise.

Maybe it would help if I describe it as a detailed thought experiment. The experiment takes place in four phases.

Phase 1: Alice and Bob choose a basis for a pure state P which they will use for the remaining two phases.

Phase 2: Alice teleports N copies of state P to Bob using the normal protocol, including the transmission of the results of her measurements. Bob takes the N/4 particles that require no rotation and tests them to see if they produce first-order interference relative to the basis of P. I trust you and I agree that he will observe interference in this case.

Phase 3:

This is the part that can't be realized in practice, and I have to number the steps here because this phase runs in a loop. Phase 3 is designed to answer the question: what would have happened in phase 2 if Bob had chosen the same N/4 particles by pure chance? So...

1. N EPR pairs are distributed.

2. Alice performs her part of the teleportation protocol, but does NOT tell Bob the results of her measurements.

3. Bob selects N/4 particles at random and tests for first-order interference relative to P. (The vast majority of the time the result will be negative.)

4. Bob and Alice compare Bob's random selections in step 3 with the results of Alice's measurements in step 2. If they happen to coincide, i.e. Bob just happened to pick the correct N/4 particles that did not require rotation, the experiment halts, with the result being whatever Bob observed on the last iteration of step 3.

I trust that you and I will agree that Bob will also observe interference in this case.

Phase 4 (this is the interesting one):

This is identical to phase 3, except that steps 2 and 3 are reversed, i.e. Bob makes his random selection and interference measurement BEFORE (in a fully relativistic sense) Alice makes her measurements. i.e.:

1. N EPR pairs are distributed.

2. Bob selects N/4 particles at random and tests for first-order interference relative to P.

3. Bob communicates to Alice that he is done.

4. AFTER Alice receives Bob's signal from step 3, she performs her side of the teleportation protocol for N copies of P.

5. They compare the results of Alice's measurements in step 4 with Bob's random choices made in step 2. If they coincide (i.e. Bob just happened to choose the correct N/4 particles that did not require rotation) the experiment concludes, with the result being whatever Bob observed on the final iteration of step 2. Otherwise, they go to step 1 and try again.

On your view, the predicted result of phase 4 will be negative. So if Alice cheats and performs her measurements before receiving Bob's signal, Bob can tell.

Postscript: now that I think about it, it might actually be possible to perform this experiment. A mach-zehnder interferometer can be pretty sensitive, so it might be possible to get N down low enough that the experiment could terminate in a reasonable amount of time.