Cosmic Bell Test: Measurement Settings from Milky Way Stars

Bell’s theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell’s inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this “freedom of choice” was addressed by ensuring that selection of measurement settings via conventional “quantum random number generators” was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell’s inequality that, for the first time, uses distant astronomical sources as “cosmic setting generators.” In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon’s color was set at emission, we observe statistically significant $\gtrsim 7.31\sigma$ and $\gtrsim 11.93\sigma$ violations of Bell’s inequality with estimated $p$ values of $\lesssim 1.8\times {10}^{-13}$ and $\lesssim 4.0\times {10}^{-33}$, respectively, thereby pushing back by $\sim 600\text{years}$ the most recent time by which any local-realist influences could have engineered the observed Bell violation.

Figure 1

(a) The three experimental stations and related acronyms are described in the main text. Stellar photon receiving telescopes (Rx-SP) with primary mirror diameters of 0.2032 m (Meade 8-inch LX200 ACF, $f=2\mathrm{m}$) and 0.254 m (Meade 10-inch LX600 ACF, $f=2.032\mathrm{m}$) were used by Alice and Bob, respectively, although the telescope apertures were each partially covered to limit sky noise. Diameters and focal lengths of the quantum channel telescopes are Alice (Tx-EP: $d=50.8$, $f=100\mathrm{mm}$; Rx-EP: $d=80$, $f=400\mathrm{mm}$) and Bob (Tx-EP: $d=70$, $f=280\mathrm{mm}$; Rx-EP: $d=140$, $f=420\mathrm{mm}$). Latitude, longitude, and elevation for the three experimental sites are Alice ($A$: 48.21645°, 16.354311°, 215.0 m), Bob ($B$: 48.23160°, 16.3579553°, 200.0 m), and the Source ($S$: 48.221311°, 16.356439°, 205.0 m). (b) and (c) For experimental run 1, the setup deviated from the ideal, colinear 1D case by the angles displayed. Site coordinates yield $\alpha \approx 180°$ and $\beta \approx 169°$ for both runs. See Table 1 for the azimuth (az) and altitude (alt) of each star observed during each experimental run. (3D graphics taken from Google Earth, 2016.)

Figure 2

$(1+1)\mathrm{D}$ space-time diagram for run 1, with the origin at the entangled pair creation (black dot) and a spatial projection axis chosen to minimize its distance to Alice and Bob. After a fiber delay (thick black line), entangled photons are sent via free-space channels (thin black lines) to be measured by Alice and Bob at events $A$ and $B$. Blue and red stars indicate example valid settings from measuring stellar photons emitted far away at space-time events $A_{\star }$ and $B_{\star }$ (see Fig. 3). Ensuring locality limits valid settings to the shaded regions. Delays to implement each setting and an added safety buffer shorten the validity time windows actually used to the darker shaded regions.

Figure 3

$(2+1)\mathrm{D}$ space-time diagram for run 1 with past light cones for stellar emission events $A_{\star }$ and $B_{\star }$. Two spatial dimensions are shown ($x\text{−}y$ plane) with the third suppressed. The stellar pair’s angular separation on the sky is the angle between the red and blue vectors. Our data rule out local-realist models with hidden variables in the gray space-time region. We do not rule out models with hidden variables in the past light cones for events $A_{\star }$ (blue), $B_{\star }$ (red), or their overlap (purple).

Figure 4

For run 1, bars show the correlation $E_{ij}$ for each joint setting combination $(a_i,b_j)$. CHSH terms are displayed with negative signs (red) and a positive sign (green), showing that our data violate the local-realist bound (dashed line, $S=2$). The $|E_{ij}|$ values are unequal due to limited state visibility and imperfect alignment of the polarization measurement bases.