"Let us illustrate the problem of signalling with the assistance of the ubiquitous experimenters Alice and Bob. We will place Alice and Bob at some distance apart, and between them there will be a source emitting pairs of entangled particles. To avoid relativistic complications we will assume that Alice, Bob, their detectors, and the particle source are all mutually at rest in an inertial frame (the ‘lab’ frame). Pair after pair of particles are emitted by the source and detected by Alice and Bob's apparatuses, who record their results. Alice and Bob are free to alter the angle of their detectors with each run of the apparatus.

What each experimenter will record is an apparently random sequence of ups and downs, like the results of an honest coin repeatedly tossed; and yet, when they compare results afterward, they will note that certain correlations, generally sinusoidal in form, stand between their results. For example, if the particles are spin-1/2 fermions, and if Alice and Bob are measuring spin in a particular direction, then the correlation between their results will be -cos@ where @ is the angle between Alice and Bob's detectors. Sinusoidal correlations like these readily violate mathematical inequalities such as those defined by Bell (1964). Itamar Pitowsky (1994) showed that the Bell Inequalities are examples of “conditions of possible experience” first written down by George Boole; these are consistency conditions between measurement results on the assumption that the results of one measurement and the way it is carried out does not influence the measurement of the other particle at the time of measurement. This means that the particular sequence of results that Alice and Bob get at their respective detectors could not have been encoded in the particles at the source; for some relative angles their results are too well correlated or anti-correlated for them to be due to local causes built into both particles when they were emitted” Kent Peacock "The No-Signalling Theorems: A Nitpicking Distinction”

Here is the setup

Bob is closer to the pair source S than Alice.

B — S—————A

Bob does not change his settings.

Alice at the last moment changes her settings in delayed choice fashion AFTER Bob’s particles in the entangled pairs has already been detected.

This is done in pulse fashion so that there is a good statistical sample of particles in each pulse.

Each setting (ai,b) b-fixed has random outputs 1,0 for each individual detection.

Using the statistical rules of orthodox quantum theory Alice and Bob compare their raw data after the experiment is over and from the fraction of coincidences in each pulse, Bob can infer the sequence of settings a1, a2, …. aN for N pulses, which is the encoded message.

It is obvious, since Bob did nothing at all, that Alice’s free will choices of settings a1, a2, …. aN for N pulses (which is the message) is the active future cause of the back-from-the-future coincidences, unless you want a paranoid conspiracy theory.

Now of course this is not Valentini’s “signal nonlocality” that is a larger theory violating orthodox quantum theory the way general relativity violates special relativity globally though not locally. With Valentini’s PQM extension of QM Bob can know in advance what Alice will choose even before she chooses it without doing the hindsight correlation analysis. However, any attempt by Bob to cause a paradox will fail either for reasons given by Thorne and Novikov or by David Deutsch.