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Consider the wave function collapse of a pair of entangled photons:

  • wave function is collapsed, let's call this state '0'

  • normal wave function, let's call this state '1'

In a "delayed choice" experiment, future action on one photon modifies past state of the other photon: it will either be in state 0 or 1 depending on what happens in the experiment few moments after.

Is it safe to assume that 1 bit of information is sent back in time?

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  • $\begingroup$ It's safe to assume that there is some kind of conservation of information going on. If you know the path of the photons, you get a particle result and if you don't know the path of the photons, you get a wave result, REGARDLESS of how cleverly you design the experiment. $\endgroup$ – David White Oct 9 at 19:13
  • $\begingroup$ Measurement of one member of a pair of entangled particles does not send information anywhere. Instead, the measurement determines information about both particles. Wave function collapse refers to the measurement process itself, in which one out of multiple possible states is detected. $\endgroup$ – S. McGrew Oct 9 at 19:50
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No, that is not a safe assumption. The class of experiments you refer to tend to have two measurements taking place at different times, in such a way that it is possible to interpret the later measurement as influencing the outcome of the earlier one. However, there is in each case a reciprocity that allows you equally to consider that the earlier measurement was the cause of the later one- ie either measurement implies the other. There is no reason, therefore, to invoke the possibility of reverse causality in order to explain the result.

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I’m going to expand on Marco’s (correct) answer a bit.

In the DCQE, remember that the recovered interference patterns from the “no which-way info” arms of the experiment are complimentary - e.g. the bright bands of one arm would line up with the dark bands of the other arm.

This is very important - it means that when you first detect an entangled photon at a location (x,y) on your “idler” detection plate, you can say with certainty that at least one possible option is off the table for where the sister photon will later be found:

Using the notation from the Wiki article on the Kim et al setup, if your idler defector receives a photon at an (x,y) that corresponds to a trough in the interference pattern recovered from coincidence counting with the D1 detector, you can have high confidence that the sister photon will show up at either D3, D4, or D2 (since these 3 produce patterns still consistent with where your idler photon showed up on D0).

So far from requiring any spooky retrocausality, you can see that the photon arriving at D0 provides you enough information to update your expectations about where it’s entangled sister may be found in the future. That’s all.

The choice to measure either which-way or interference will then only further reduce the options for where the signal photon can be detected. Choose to measure which-way, and you’ve now got high confidence it can only be detected at either D3 or D4. Measure interference, and you can be confident that it’ll show up at D2 (because again, the location on D0 you already know corresponds to a dark band for the D1 recovered interference pattern).

The choice of whether to measure interference or not has nothing to do with retrocausality or anything of the sort - it can be described purely in forward-working reductions in possibilities as you gain more info about the system - first based on the D0 reading, and next based on your choice of what to measure.

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