Does this recent Zeilinger group delayed choice entanglement experiment imply backward-in-time influences?
From the abstract: "This can also be viewed as “quantum steering into the past ”."
No, there is no retrocausal causation in the delayed choice entanglement swapping experiment (or any other experiment or process in the Universe, for that matter), see
for a detailed explanation. Correlations between Alice, Bob, and Victor's outcomes may obviously be verified only after all of them complete their measurements.
But one may easily prove – by a simple application of the completeness relation i.e. independence of some inner product on the choice of bases – that if Alice and Bob measure their particles before Victor, their outcomes (the probabilistic distributions governing them) will be totally unaffected by Victor's later decisions. For this reason, the cause behind correlations in any group – for example the group of four photons in this experiment – is always hiding in the fact that these components have been in contact in the past. Correlation isn't causation, at least not a randomly picked causation, and there's never any causation between spacelike-separated events and there's never any causation that would go backwards in time, either. Quantum mechanics fully respects this statement.
Also, Heisenberg's equations make it totally obvious that the degree of entanglement between two isolated subsystems isn't changing with time. In fact, this experiment is really designed so that the polarizations of any of the photons don't change with time at all after the photons are produced in the special four-photon initial state. This makes it obvious that the results of the measurements don't depend on the timing of the measurements and it makes it silly to be surprised by this independence on the timing.
In all such bizarre nonlocal or retrocausal interpretations of quantum measurements, the error hides in the people's attempts to create a "classical model" which already possesses objective properties before they are measured. But there's no valid classical model that would coincide with the Universe, a system that respects inequivalent, quantum rules. One must carefully wait for the moment of the measurements but whenever we learn the results of the measurements, the most accurate predictions of probabilities of new, future experiments has to take all the previously measured outcomes into account; we must switch to the appropriate conditional probabilities which some people materialistically interpret as "collapsing wave function".
So if Victor does the experiment after Alice and Bob and he wants the most accurate predictions, he must "collapse the wave function" for his photons according to the results obtained by Alice and Bob. If he doesn't know these results, he won't be able to collapse them and he will only predict things according to the initial distribution. Whether he knows something or not, quantum mechanics unambiguously predicts that there would be correlations between the outcomes obtained by Alice, Victor, and Bob and no retrocausal influences are needed in quantum mechanics to produce these – experimentally verified – predictions.
"...and there's never any causation between spacelike-separated events" The integral form of the Schrödinger equation is over all space. If there is no action at a distance, then AFAICS it is wrong. My understanding is that this was the basis of Einstein's issue with QM and he (and others) designed the EPR experiment to prove QM was incorrect but when it was performed it only confirmed QM.
A pretty good non-technical summary of the experiment and its possible interpretations is given by Chad Orzel here: