Random Number Generation with Cosmic Photons

Random numbers are indispensable for a variety of applications ranging from testing physics foundations to information encryption. In particular, nonlocality test provide strong evidence for our current understanding of nature—quantum mechanics. All the random number generators (RNGs) used for the existing tests are constructed locally, making the test results vulnerable to the freedom-of-choice loophole. We report an experimental realization of RNGs based on the arrival time of cosmic photons. The measurement outcomes (raw data) pass the standard NIST statistical test suite. We present a realistic design to employ these RNGs in a Bell test experiment, which addresses the freedom-of-choice loophole.

Figure 1

Random number generation with cosmic photons. Photons from a cosmic radiation source under study with wavelength in the range [680, 830] nm are collected into a multimode optical fiber for RNG. Inset: Photons with wavelength in the range [530, 680] nm, form an image of the CRSS, here, quasar IGR $\mathrm{J}03334+371$ is on the camera for tracking. Astronomy applications (APP).

Figure 2

Experimental true signal rate (background subtracted) versus magnitude. The trend line (solid) is fitted with data (open square) for magnitude $<11$, and extrapolated to magnitude 16 (dashed line). The shaded regions indicate 2 standard deviations, with the one on the horizontal axis for background. Solid red dot: data for quasar IGR $\mathrm{J}03334+371$.

Figure 3

Space-time diagram of an event-ready Bell test experiment with NV centers [6, 14]. $S1$ and $S2$ are cosmic photon emission events, followed by events $R1$ and $R2$ to output random bits for base choice. $P1$ and $P2$ are events for NV centers to send photons for Bell state measurement after the creation of entangled photon-electron pairs (EPR1,2) at NV centers. The photons are sent for BSM via optical fibers, shown by red lines. A destructive BSM with photons from the two entangled electron-photon pairs prepares the two electrons in a Bell state, which is ready for state measurements ($M1$ and $M2$) after the base choice. $Y1$, $Y2$, and $Y3$ are local correlation events (denoted by local hidden variables, $\lambda 1$, $\lambda 2$, $\lambda 3$) that may occur in the overlapped region formed by the past light cones (see text for details).

Figure 4

Schematic of an event-ready Bell experiment. Each measurement station (Lab1 or Lab2) prepares an entangled electron-photon pair with a NV center. Lab1(2) down-converts single photons from visible to infrared (1550 nm) via difference frequency generation (DFG). A successful BSM with a single photon from Lab1 and a single photon from Lab2 projects the corresponding two electrons into a Bell state. RNG1 and RNG2 provide random bits per time window $T_W$ to set the base in measuring the quantum state of the electron spin. $\alpha 1$ and $\alpha 2$ are angles of the optical axes of telescopes with respect to the Lab axis (see Supplemental Material [10]).