Experimental measurement-dependent local Bell test with human free will

A Bell test can rule out local realistic models and has potential applications in communication and information tasks. For example, a Bell's inequality violation can certify the presence of intrinsic randomness in measurement outcomes, which can be used to generate unpredictable random numbers. Nevertheless, a Bell test requires measurements that are chosen independently of environment in the test, as would be the case if the measurement setting choices were themselves intrinsically random. Such situation seems to create a “bootstrapping problem” recently addressed in the BIG Bell Test, a collection of various Bell tests using human choices. Here, we report in detail our experimental methods and results within the BIG Bell Test, specifically for a special type of Bell inequality, known as the measurement-dependent local inequality. With this inequality, even a small amount of measurement independence makes it possible to disprove local realistic models. The experiment utilizes human-generated random numbers in selecting the measurement settings and is implemented with space-like separation between two distant measurement sites. The experimental result violates a Bell's inequality, which cannot be explained by local hidden variable models with independence parameter (as defined in [G. Pütz et al., Phys. Rev. Lett. 113, 190402 (2014)]) $l>0.10\pm 0.05$. This result further quantifies the degree to which a local hidden variable model would need to constrain human choices, if it is to reproduce the experimental results.

Figure 1

Bell test with imperfect input randomness.

Figure 2

Bell test using imperfect input randomness. (a) Positions of the entanglement source, Alice's and Bob's detection. Distance between the source and Alice (Bob) is $87\pm 2$ m $(88\pm 2$ m). (b) Schematic setup of the Bell test. A distributed feedback (DFB) laser diode (LD) at $\lambda =1560$ nm is modulated at 100 kHz with 10 ns width. The pulse is amplified with an erbium-doped fiber amplifier (EDFA) and then up-converted to 780 nm via a second-harmonic generation (SHG) in an in-line periodically poled lithium niobate (PPLN) waveguide. The residual 1560 nm light is filtered with a wavelength-division multiplexer (WDM) and a filter. After polarization adjustment using a half-wave plate (HWP) and a liquid crystal (LC), the 780 nm pump light is focused to a periodically poled potassium titanyl phosphate (PPKTP) crystal in a Sagnac setup to generate entangled pairs. A series of dichroic mirrors (DMs) are used to remove the residual pump light at 780 nm and the fluorescence before the entangled pairs are collected. In Alice's and Bob's detection station, a polarization controller (PC), a quarter-wave plate (QWP), a HWP, and a polarizing beam splitter (PBS) are used to align the reference frame. Random numbers control the Pockels cell to dynamically select the bases. Superconducting nanowire single-photon detectors (SNSPDs) are used to detect the photons after the PBS.