Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars

In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell’s inequality by 9.3 standard deviations, corresponding to an estimated $p$ value of $\lesssim 7.4\times {10}^{-21}$. This experiment pushes back to at least $\sim 7.8\mathrm{Gyr}$ ago the most recent time by which any local-realist influences could have exploited the “freedom-of-choice” loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.

Figure 1

The experimental stations for our cosmic Bell test. Alice’s station received cosmic photons with the Telescopio Nazionale Galileo (TNG), whose primary mirror diameter is 3.58 m, while Bob’s station received cosmic photons with the William Herschel Telescope (WHT), whose primary mirror diameter is 4.20 m. Polarization entangled photons were sent from the source to Alice and Bob. Diameters and focal lengths of the quantum channel telescopes were Tx: $d=70\mathrm{mm}$, $f=280\mathrm{mm}$; Rx: $d=140\mathrm{mm}$, $f_{\mathrm{eff}}=1470\mathrm{mm}$. Latitude, longitude, and elevation for the experimental sites were Alice ($\mathcal{A}$: 28.75410°, $-17.88915°$, 2375 m), Bob ($\mathcal{B}$: 28.760636°, $-17.8816861°$, 2352 m), and the Source ($\mathcal{S}$: 28.757189°, $-17.884961°$, 2385 m). The distances from Source to Bob and Alice were 500 and 534 m, respectively.

Figure 2

A photon pair source located in the middle produced polarization-entangled photons at center wavelengths of 773.6 and 850 nm. The photons were separated into two spatial modes via a dichroic mirror and sent via free-space channels to the quantum receivers at Bob (773.6 nm) and Alice (850 nm). Fast steering mirrors guided the photons to the receivers using a green LED as a reference. Electro-optical modulators (EOM) rotate the measurement basis according to the input signals from the CRNGs. Polarization measurements are performed using a polarizing beam splitter (PBS) with avalanche photodiodes in each output path. Detection events are time stamped by the control and data acquisition unit (CaDa) and stored locally. Quasar light is collected by the astronomical telescopes and fed into an optical system that creates a magnified image with an iris to restrict the field of view. The quasar light is then split according to its wavelength into a “blue” and a “red” channel, whereby each channel contains additional filters to remove misdirected photons. The detector signals are used to trigger the implementation of the corresponding measurement basis at the EOM.

Figure 3

$(1+1)\mathrm{D}$ space-time diagram for pair 1, with the origin at the source $\mathcal{S}$ of entangled pair creation (black dot) and a spatial projection axis chosen to minimize its distance to Alice and Bob. After a short fiber delay (too small to see), entangled photons are sent via free-space channels (black lines) to be measured by Alice and Bob at events $A$ and $B$. Galaxy symbols indicate examples of measurements of valid settings from quasar photons emitted far away at space-time events ${\mathcal{Q}}_A$ and ${\mathcal{Q}}_B$. Ensuring locality limits settings to the shaded regions. Delays to implement each setting and an added safety buffer shorten the validity time windows that were actually used to the darker shaded regions.

Figure 4

$(2+1)\mathrm{D}$ space-time diagram for pair 1, showing the past light cone of our experiment (gray) and of the quasar emission events ${\mathcal{Q}}_{\mathcal{A}}$ (blue) and ${\mathcal{Q}}_{\mathcal{B}}$ (red), extending back to the big bang, 13.80 Gyr ago. The quasars in pair 1 emitted the light that we observed during our experiment $t_{\mathrm{lb}}^{\mathcal{A}}=7.78\mathrm{Gyr}$ and $t_{\mathrm{lb}}^{\mathcal{B}}=12.21\mathrm{Gyr}$ ago. The past light cones from ${\mathcal{Q}}_{\mathcal{A}}$ and ${\mathcal{Q}}_{\mathcal{B}}$ last intersected $t_{\mathrm{lb}}^{\mathcal{A}B}=13.15\mathrm{Gyr}$ ago. The shapes of the light cones reflect the changing rate of cosmic expansion since the big bang. To be consistent with our data, any local-realist mechanism would need to have affected detector settings and measurement outcomes of our experiment from within the past light cones of events ${\mathcal{Q}}_{\mathcal{A}}$, ${\mathcal{Q}}_{\mathcal{B}}$, or their overlap, a space-time region that consists of only 4.0% of the physical space-time volume contained within the past light cone of our experiment. Such a local-realist scenario would need to have been set in motion at least 7.78 Gyr ago.