---
title: "Delayed-choice swapping: later labels, earlier records"
description: "What changes when the joint analyzer is chosen after the outer photons have been detected?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/delayed-choice-swapping-sorted-records/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/delayed-choice-swapping-sorted-records/"
last_modified: "2026-10-18"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Delayed-choice swapping: later labels, earlier records

Sandbox Physics · 2026-10-18

What changes when the joint analyzer is chosen after the outer photons have been detected?

## Build a timeline before a story

Ma and colleagues’ 2012 experiment registered the outer photons before a randomly controlled analyzer choice and measurement on the central photons. Fiber delays and a fast tunable analyzer established the ordering. The paper places the later choice in the timelike future of the earlier detections.

The reported paths included seven-metre fibers to the outer stations and 104-metre delays for the central photons. Those lengths belong to a complete timing design with switching and registration intervals; subtracting lengths alone is not an independent proof of the spacetime claim. Delayed choice also does not mean spacelike separation.

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834 X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction

## What the later station supplies

The central station could choose a Bell-state analysis or a separable polarization analysis. Its setting and outcome supplied labels for sorting already stored outer records. The appropriate subsets then supported different conditional correlations, rather than requiring that earlier detector files be edited.

For fixed outer settings, denote their two outcomes by the two lowercase letters below, the central outcome by the third and the central choice by the final letter. Summing over every central outcome restores the unsorted distribution. In the ideal model that marginal is independent of the later choice; losses require a complete outcome category as well.

$$
\begin{gathered}\sum_c P(a,b,c\mid y)=P(a,b)\\[4pt]P(a,b\mid c,y)=\frac{P(a,b,c\mid y)}{P(c\mid y)}\end{gathered}
$$

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834

## A ledger with four equally likely labels

For two ideal positive Bell input pairs, the four central Bell outcomes are equally likely. In the horizontal–vertical outer basis, two labels select equal outcomes and two select opposite outcomes. Each label gives a definite correlation pattern, yet the unsorted table has all four outcome pairs equally often.

In an invented ledger of four hundred ideal trials, take one hundred of each central label. The combined outer table has one hundred events in each cell. Sorting changes which cells contribute to a subset; it does not change any stored outcome. The same argument works when central measurements are evaluated after outer measurements because they act on different subsystems.

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834

## Certify more than a preferred correlation

The experiment compared correlations in three complementary polarization bases and used a Bell-state fidelity witness. For any separable two-qubit state, overlap with a chosen maximally entangled Bell state cannot exceed one half. Fidelity above that bound is therefore sufficient for entanglement under the calibrated measurement model.

The corrected witness is half the identity minus the target Bell projector, so its expectation is negative exactly when that target fidelity exceeds one half. A nonnegative result does not prove separability: an entangled state can have little overlap with the particular target. The journal’s correction notice makes checking the sign especially important here.

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834 X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction

## Sorting is not a message to the past

To recover the conditional subsets, the outer stations need the central labels through an ordinary classical channel. Before those labels arrive, their files contain the same unsorted statistics. Choosing a later setting cannot place a chosen message in an earlier station’s local data.

A useful audit preserves timestamps, basis choices, every outcome category and the event-matching rule. A change in a selected subset’s rate can otherwise be mistaken for a change in the unconditional distribution. No-signalling is a statement about the complete marginal; it is not a claim that every postselected plot must look unchanged.

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834 M. Żukowski, A. Zeilinger, M. A. Horne and A. K. Ekert (1993), Event-Ready-Detectors Bell Experiment via Entanglement Swapping, PRL 71, 4287–4290

## Keep the experimental scope

The delayed-choice result tests conditional quantum predictions in a demanding timing arrangement. It does not by itself select an interpretation of quantum mechanics, demonstrate controllable retrocausality or certify a loophole-free Bell experiment. Those are different claims with additional conditions.

The quantum eraser Lab supplies a related exercise in complementary event groups; its scene is not this four-photon apparatus. Use the swapping reading for the initial pairs and the tomography reading for calibrated inference. The question remains concrete: which complete record was stored, and which later label made a conditional statement possible?

Read the evidence: X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834 X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction

## Continue with the models

These are existing teaching Labs. Their simulated records are separate from the historical observations discussed above.

- [Compare complementary groups of fixed records](https://sandboxphysics.com/labs/quantum-eraser/)
- [Keep a Bell test’s sampling assumptions separate](https://sandboxphysics.com/labs/bell-chsh/)

## Sources and reading notes

We consulted Ma et al.’s 17-page arXiv manuscript, especially the event ordering, optical delays and three-basis verification. The journal page records a 26 April 2012 correction to the witness definition; we use the corrected negative-witness convention. The ideal probability identities and example below are our calculations, not a reanalysis of the experimental data.

1. [M. Żukowski, A. Zeilinger, M. A. Horne and A. K. Ekert (1993), Event-Ready-Detectors Bell Experiment via Entanglement Swapping, PRL 71, 4287–4290](https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.71.4287)
2. [X.-S. Ma et al. (2012), Experimental delayed-choice entanglement swapping — author manuscript, arXiv:1203.4834](https://arxiv.org/pdf/1203.4834)
3. [X.-S. Ma et al., Nature Physics 8, 479–484 (2012) — journal record and 26 April 2012 witness correction](https://www.nature.com/articles/nphys2294)

[Blackbody radiation: a whole curve, not one quantum](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/) [Photoelectric evidence: the voltage is not yet the energy](https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/) [Oil drops: finding a charge unit in falling times](https://sandboxphysics.com/stories/quantum-evidence/millikan-oil-drop-charge-inference/) [Atomic spectra: evidence for states, not photographs of orbits](https://sandboxphysics.com/stories/quantum-evidence/atomic-spectra-stationary-states/) [Franck–Hertz: what a falling current can establish](https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/) [Compton scattering: light must balance momentum too](https://sandboxphysics.com/stories/quantum-evidence/compton-scattering-energy-momentum/) [de Broglie: a wavelength for matter, a speed for the packet](https://sandboxphysics.com/stories/quantum-evidence/de-broglie-matter-waves-phase-packets/) [Matrices and waves: two routes to the same predictions](https://sandboxphysics.com/stories/quantum-evidence/matrix-wave-mechanics-observables/) [Born: how a scattering direction became a probability](https://sandboxphysics.com/stories/quantum-evidence/born-scattering-probability/) [Pauli: count the states before filling the shells](https://sandboxphysics.com/stories/quantum-evidence/pauli-spectra-exclusion-principle/) [Dirac’s electron: a successful equation with an unfinished story](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/) [Zeeman lines: polarization belongs to the evidence](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/) [The Stark effect: an electric field changes the spectrum](https://sandboxphysics.com/stories/quantum-evidence/stark-effect-electric-field-spectra/) [Canal rays: moving light does not identify the emitter by itself](https://sandboxphysics.com/stories/quantum-evidence/stark-canal-rays-doppler-emitters/) [Stern–Gerlach: two traces, then a new interpretation](https://sandboxphysics.com/stories/quantum-evidence/stern-gerlach-silver-beam-spin/) [Stern’s proton moment: a small deflection with a large consequence](https://sandboxphysics.com/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/) [Magnetic resonance: three ways to notice a transition](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/) [Optical pumping: make a population difference visible](https://sandboxphysics.com/stories/quantum-evidence/optical-pumping-populations-double-resonance/) [The Lamb shift: a missing signal reveals a missing correction](https://sandboxphysics.com/stories/quantum-evidence/lamb-shift-microwave-evidence/) [Kusch and Foley: a small mismatch between magnetic factors](https://sandboxphysics.com/stories/quantum-evidence/kusch-foley-electron-magnetic-moment/) [Mössbauer resonance: recoil has not disappeared](https://sandboxphysics.com/stories/quantum-evidence/mossbauer-recoil-free-resonance/) [Ramsey and ion traps: make time to measure](https://sandboxphysics.com/stories/quantum-evidence/ramsey-ion-traps-measurement/) [Ramsey clocks: a stable fringe can carry a phase bias](https://sandboxphysics.com/stories/quantum-evidence/ramsey-cavity-phase-frequency-bias/) [Quantum projection noise: better detection still leaves a random count](https://sandboxphysics.com/stories/quantum-evidence/quantum-projection-noise-population-counts/) [Fountain clocks: the density ratio is part of the correction](https://sandboxphysics.com/stories/quantum-evidence/fountain-clock-collision-density-extrapolation/) [Paul’s trap: stability comes from the changing field](https://sandboxphysics.com/stories/quantum-evidence/paul-trap-dynamic-stability-micromotion/) [Dehmelt’s single electron: spin appears as an axial frequency shift](https://sandboxphysics.com/stories/quantum-evidence/dehmelt-single-electron-penning-spin-readout/) [Laser cooling: when the temperature contradicted the model](https://sandboxphysics.com/stories/quantum-evidence/laser-cooling-below-doppler-limit/) [Zeeman slowing: keep a moving atom within reach of the light](https://sandboxphysics.com/stories/quantum-evidence/zeeman-slowing-neutral-atom-beam/) [Chu’s optical molasses: slowing motion while atoms still escape](https://sandboxphysics.com/stories/quantum-evidence/chu-optical-molasses-diffusion-escape/) [Cold-atom thermometry: read the flight, then infer the temperature](https://sandboxphysics.com/stories/quantum-evidence/cold-atom-ballistic-thermometry/) [Sisyphus cooling: where the energy leaves the hill](https://sandboxphysics.com/stories/quantum-evidence/sisyphus-cooling-polarization-energy/) [Subrecoil cooling: two narrow peaks are not zero motion](https://sandboxphysics.com/stories/quantum-evidence/subrecoil-cooling-dark-state-momentum/) [A dark interval from one ion: reading electron shelving](https://sandboxphysics.com/stories/quantum-evidence/electron-shelving-single-ion-jumps/) [Unequal sidebands: how cold is a trapped ion?](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/) [Quantum logic spectroscopy: let another ion report the answer](https://sandboxphysics.com/stories/quantum-evidence/quantum-logic-spectroscopy-shared-motion/) [Single quantum systems: what survives a measurement?](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/) [A cavity cat loses coherence before it loses its energy](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/) [Counting stored light: one atom gives a clue](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/) [Quantum feedback: a target needs more than an estimate](https://sandboxphysics.com/stories/quantum-evidence/quantum-feedback-photon-number-verification/) [Bell tests: correlations need an experimental contract](https://sandboxphysics.com/stories/quantum-evidence/bell-tests-correlations-loopholes/) [Freedman–Clauser: the denominator belongs to the experiment](https://sandboxphysics.com/stories/quantum-evidence/freedman-clauser-coincidence-normalization/) [Aspect’s switches: read the spacetime before the slogan](https://sandboxphysics.com/stories/quantum-evidence/aspect-switching-spacetime-records/) [An event-ready Bell test: count the trials before the wins](https://sandboxphysics.com/stories/quantum-evidence/event-ready-bell-trials-finite-statistics/) [Photon Bell tests: the trials with no clicks still count](https://sandboxphysics.com/stories/quantum-evidence/photon-bell-losses-optical-trials/) [GHZ correlations: four settings, no consistent instruction table](https://sandboxphysics.com/stories/quantum-evidence/ghz-parity-three-photon-records/) [Teleportation: read the conditions before the coincidence](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/) [Heralded photons: the missing coincidences need a denominator](https://sandboxphysics.com/stories/quantum-evidence/heralded-photon-anticorrelation-gates/) [The Hong–Ou–Mandel dip: which alternatives became indistinguishable?](https://sandboxphysics.com/stories/quantum-evidence/hong-ou-mandel-dip-mode-overlap/) [Entanglement swapping: four clicks define the selected pair](https://sandboxphysics.com/stories/quantum-evidence/entanglement-swapping-fourfold-records/) [Dense coding: three messages and a resource ledger](https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/) [Photon tomography: a physical matrix still needs calibrated counts](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)