If there was truly zero entanglement prior to and throughout the experiment until Wigner made his own measurement, then he ought to see interference effects as Deutsche originally intended. However by communicating with his friend, e.g. by exchange of photons or electrons, directly or indirectly, after his friend had branched, he would see no such interference effects. It just isn't possible to separate Wigner out of the wavefunction the way you think we can. — Kenosha Kid

So, on your view, Deutsch's thought experiment fails?

For reference, Deutsch's thought experiment is in section 8 (p32) with the interference experiment (distinguishing MWI from objective collapse CI) described on pp35-36.

Sorry Andrew, I missed your post. I'll have a re-read when I get a mo, but iirc the friend records that a measurement had taken place but remains unentangled with Wigner because no communication occurs. If I'm wrong about that, and Deutsch insists that the two friends can communicate and remain uncorrelated, then yes I'd disagree with him. He'd essentially be saying you could put a person into quantum superposition (branching) but treat him as a classical object (remain factorisable after exchanging particles).

I'll have a re-read when I get a mo, but iirc the friend records that a measurement had taken place but remains unentangled with Wigner because no communication occurs. — Kenosha Kid

Yes. Then, in Deutsch's thought experiment, Wigner performs a unitary operation that undoes the friend's measurement while preserving that record. The preserved record is essentially a single qubit of information that was flipped from |0> to |1> by the friend in both branches. Deutsch says:

But in particular, the record that the N-S value of the spin was known to the observer at time t''' is preserved.

At this point, t'''', according to the Everett interpretation, all copies of the observer are once again identical though they had been different in two branches at time t''' (69): — Quantum Theory as a Universal Physical Theory - David Deutsch, p36

So the friend themselves (the observer in the above quote) can determine that the qubit is set to |1> which demonstrates for her, as well as for Wigner, that she had made a definite measurement.