This question was bumped by the Community bot, so I am supplying an answer. Better late than never?
- This is a clever question and has some good points mixed in. To answer the main question:
a) Assuming either Alice (or Bob) individually could detect entanglement using the technique described by the paper of Pezze et al (2016): Alice (and Bob) would ALWAYS detect an entangled state regardless of what Victor does. So no signal can be sent by Victor.
The reason: All 4 photons in a delayed choice entanglement experiment start out entangled. Yes, Victor can choose to swap entanglement to 1 & 4, but otherwise 1 & 2 are entangled and 3 & 4 are entangled. Either way, Alice sees nothing but entangled photons.
b) Suppose we need Alice and Bob to collectively use the Pezze protocol. The hypothetical "statistical speed" velocity(delta theta)^2 - I'll call that V for simplicity - is based on timing of the arrival time (detection) of their respective photons (1 & 4) - specifically related to the difference in arrival times of each 1 & 4 pair as a function of V. Actually V - a very small number in the ideal case - becomes the standard deviation of a collection of trials between V and what they call Vmax. Let's call that V*, see for example their equations (9) and (10) to get a better idea, and Figure 2 as well. We are talking a microscopically small number.
But in fact, those arrival times do not necessarily mean anything at all. Normally, the arrival times of photons seen by Alice and Bob are within a coincidence time window of perhaps 5 nanoseconds. (Keep in mind that the window is adjusted for each photon's path length from source to detector.) Oh, and for an entanglement swap to operate, you need separated source entangled pairs - they cannot come from the same source at the same time or they will be in a GHZ state instead of the required Bell state.
Now, it is possible - actually required - that the newly created 1 & 2 pair and the 3 & 4 pair must be synchronized as to phase. Thus their time of creation must be a integer multiple N relative to the wavelength. That distance would be on the order of 400 nanometers, times N times c. And in fact in some experiments it has been possible to limit the difference in time of emission to a small pulse (translating to pairs emitted very close in time). But there will be a difference, sometimes with Alice's pair created first, and sometimes Bob's pair created first. The sequence and N are random. In principle, with enough iterations, you might get something close to a small average difference in creation times (let's call that CT). But it is almost certain to dwarf our V* number.
But even that doesn't help us much, no matter how small CT is. That's because we also have issues with detection times. Current photon detector technology is in the sub-nanosecond range, depending on a variety of factors. With one detector each for Alice and Bob, that's a lot of detection time (let's call that DT) difference to consider.
When we are considering our detection window, we only need both detection times to be close. But for consideration with the extremely small magnitude of our equation V*, the combined CT and DT differences need to be microscopically small relative to that. Looks to me as if those will will dwarf it instead.
In plain language: the margin of error in calculating the desired "statistical speed " formula will be much larger than the value itself.
c) Of course, the Pezze paper does not use the entanglement swapping protocol anyway. I don't really think it can be adapted for that, but that's just my best assessment given a minimal review. So that would be a problem of its own (finding a way to adapt to entanglement swapping).
d) Most importantly, we have assumed the theoretical basis of the 2016 Pezze paper as valid. Many papers go unpublished (this was not), and therefore there is no peer review process. Certainly, its validity - which goes against mainstream theory - can be questioned.
I had never heard of it, which alone is not proof of anything. Nor have I ever seen so much as a hint that swapped entanglement can be detected without using information from Victor to sort the data results based on the random Bell state which he records. That of course requires classical communication. That is the mainstream view.
But that paper has only been cited by 1 other work in the past 8 years. And that citation was in a paper co-authored by Pezze himself. Usually, I would expect a novel result to attract discussion from some of the thousands of papers written each month. You can judge for yourself what to make of that, and what weight to assign that.
- For the second question, I would answer a definitive NO for the totality of the reasons presented.
