Start with the timeline
The outer detectors had already clicked when the central station chose what to measure. That was the order in Ma and colleagues’ 2012 delayed-choice swapping experiment. Fiber delays held the central photons back, and a fast analyzer then switched between two kinds of joint measurement. The choice lay in the timelike future of the outer detections: an ordinary light-speed signal from those earlier events could, in principle, reach the later one.
The paper reports seven-metre fibers to the outer stations and 104-metre delays for the central photons. These lengths are part of a full timing design that also includes switching and detection times, so subtracting the lengths alone does not prove the claim about spacetime order. The distinction matters: delayed choice concerns an order in time, while spacelike separation concerns whether a light-speed signal can connect the events.
Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction
The later station supplies labels
The central analyzer could distinguish an entangled Bell-state result or measure separable polarization results. Its choice and outcome supplied labels for the outer clicks already stored. Sorting by those labels revealed different correlations in different groups. The complete, unsorted outer table stayed the same.
Fix the outer settings. In the formula below, the first two lowercase letters are the outer outcomes, the third is the central outcome and the last letter is the central choice. Summing over all central outcomes gives back the unsorted distribution. In the ideal model, that marginal does not depend on the later choice. With losses, missed detections must be counted as an outcome of their own.
Start with two ideal input pairs in a positive Bell state. The four Bell outcomes at the central station are then equally likely. Measured in the horizontal–vertical basis, the outer photons agree under two of the labels and disagree under the other two. Each label picks out a definite correlation, yet the unsorted table predicts equal probabilities for all four outcome pairs.
Imagine four hundred ideal trials. Each central label is expected about one hundred times, and the combined outer table has an expected count of one hundred in each cell; actual counts fluctuate. Sorting changes which cells go into each subset; it changes no stored outcome. The central and outer measurements act on different subsystems. Computing either one first therefore gives the same joint probabilities.
Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834
Showing entanglement takes more than one favored correlation
The experiment compared correlations in three complementary polarization bases and used a witness based on Bell-state fidelity. A separable two-qubit state can overlap a chosen maximally entangled Bell state by at most one half. A fidelity above one half therefore shows entanglement, provided the measurements behave as the calibrated model assumes.
The corrected witness is half the identity minus the projector onto the target Bell state. Its expectation value is negative exactly when the fidelity with that target exceeds one half. A value of zero or above does not prove the state separable, since an entangled state can overlap little with this particular target. Because the journal issued a correction, the sign deserves a careful check.
Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction
Sorting sends no message to the past
The outer stations can form the conditional subsets only after the central labels reach them over an ordinary classical channel. Until then, their data show the same unsorted statistics. A later choice of setting cannot write a message into an earlier station’s local data.
To check such an experiment, keep the timestamps, the basis choices, every outcome category and the rule for matching events. Otherwise a changed rate in one selected subset can be mistaken for a change in the overall distribution. No-signalling applies to the complete marginal distribution; postselected plots can still change.
The experiment brought the conditional predictions of quantum theory into an arrangement where the choice really came later. The conditional groups can differ because they select different parts of the joint data. Interpreting that result still requires the stated timing and sampling assumptions; it does not decide between interpretations of quantum mechanics or provide controllable backward signalling. Its three-basis entanglement witness relies on calibrated measurements and the stated sampling, so this demonstration is not a loophole-free, device-independent Bell test.
The earlier outcomes acquire a later classification, and the classification becomes available only after its labels arrive by a classical channel. That separation between a stored outcome and information about a group is what makes the delayed-choice arrangement possible.
Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834M. Żukowski, A. Zeilinger, M. A. Horne and A. K. Ekert (1993), Event-Ready-Detectors Bell Experiment via Entanglement Swapping, PRL 71, 4287–4290X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction