Experimental Test of Contextuality in Quantum and Classical Systems

Contextuality is considered as an intrinsic signature of nonclassicality and a crucial resource for achieving unique advantages of quantum information processing. However, recently, there have been debates on whether classical fields may also demonstrate contextuality. Here, we experimentally configure a contextuality test for optical fields, adopting various definitions of measurement events, and analyze how the definitions affect the emergence of nonclassical correlations. The heralded single-photon state, which is a typical nonclassical light field, manifests contextuality in our setup; whereas contextuality for classical coherent fields strongly depends on the specific definition of measurement events, which is equivalent to filtering the nonclassical component of the input state. Our results highlight the importance of the definition of measurement events to demonstrate contextuality, and they link the contextual correlations to nonclassicality defined by quasiprobabilities in phase space.

Figure 1

The scenario of testing the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality. A physical system is prepared in state $\rho$ and sent to a measurement device, which performs measurements of compatible observables $\{A_i,A_{i+1}\}$ and produces outcomes $\{a_i=\pm 1,a_{i+1}=\pm 1\}$. The measurement device can be set to different configurations to realize distinct contexts $\{A_i,A_{i+1}\}$. An event register records the statistics of outcomes (including potential ancillary outcomes $A_{\mathrm{anc}}=a_{\mathrm{anc}}$).

Figure 2

Experimental setup for testing the KCBS inequality with single photons and coherent light. Single photons are heralded using spontaneous parametric down-conversion; the classical light is a weak coherent state generated by a Ti:Sapphire laser and attenuated by neutral density filters (purple area). The repetition rate of the pulses is reduced by a pulse picker (1.9 MHz). The measurement device (yellow area) is realized by a linear-optical network comprising birefringent beam displacers, half-wave plates (HWPs), and avalanche photodiodes. A FPGA registers relevant events (green area) with a coincidence window of 4.5 ns. BBO denotes $\beta$-barium borate crystal, and PBS is the polarizing beam splitter.

Figure 3

(a) Experimental KCBS values (markers) and theoretical predictions (solid lines) for coherent light fields under different measurement events $E_j$: $E_1$ (triangle, blue), $E_2$ (square, red), and $E_3$ (dot, purple). The experimental result for a heralded single-photon source (HSPS) with fair sampling (pentagram, red) is also plotted for comparison. (b) Postselection probabilities for coherent light fields under different $E_j$. The error bars are too small [34] to see in the two figures.