Testing Bell’s Inequality with Cosmic Photons: Closing the Setting-Independence Loophole

We propose a practical scheme to use photons from causally disconnected cosmic sources to set the detectors in an experimental test of Bell’s inequality. In current experiments, with settings determined by quantum random number generators, only a small amount of correlation between detector settings and local hidden variables, established less than a millisecond before each experiment, would suffice to mimic the predictions of quantum mechanics. By setting the detectors using pairs of quasars or patches of the cosmic microwave background, observed violations of Bell’s inequality would require any such coordination to have existed for billions of years—an improvement of 20 orders of magnitude.

Figure 1

Schematic of proposed experiment where cosmic sources determine the detector settings in an otherwise standard Bell-type experiment.

Figure 2

Conformal diagram showing conformal time versus comoving distance for the entire history of the visible universe. In these coordinates, null geodesics appear as 45° diagonals. Light from quasar emission events $x$ and $y$ is used to determine the detector settings at events $D_1$ and $D_2$. Meanwhile, spacelike-separated from events $x$, $y$, $D_1$, and $D_2$, the source $S$ emits a pair of entangled particles that are measured at events $M_1$ and $M_2$. The quasar emission events can be at different redshifts, provided their past light cones (solid gray lines) share no overlap with each other or with the worldline of the source or detectors since the time of the hot big bang. Event $y^{\prime }$ lies within the past light cones of $y$ and $S$ and can influence both, but not $x$.

Figure 3

Optical ugriz-band [31] photon flux from quasars in the Sloan Digital Sky Survey (SDSS) [32]. Measured photometric brightness in each band was converted to an approximate photon rate and then summed. Though this is a biased sample, the optical flux of known quasars yields candidate sources and sets the scale for telescope size, distance between the entangled particle source and detectors, and quasar photon coincidence rate.

Figure 4

Effective noise temperature for various sources, including galactic emission from the Global Sky Model [39], the atmosphere from COFE [40], and the noise temperature of state-of-the-art coherent receivers. See [41] for a similar figure, along with a photon-noise plot with Planck detectors.