Experimental Fully Contextual Correlations

Quantum correlations are contextual yet, in general, nothing prevents the existence of even more contextual correlations. We identify and test a noncontextuality inequality in which the quantum violation cannot be improved by any hypothetical postquantum theory, and use it to experimentally obtain correlations in which the fraction of noncontextual correlations is less than 0.06. Our correlations are experimentally generated from the results of sequential compatible tests on a four-state quantum system encoded in the polarization and path of a single photon.

Figure 1

Graph corresponding to inequality (7). Vertices represent propositions. For example, $01|25$ means “result 0 is obtained when test 2 is performed, and result 1 is obtained when test 5 is performed.” Edges link propositions that cannot be simultaneously true. For example, $01|25$ and $01|02$ are linked, since in the first proposition the result of test 2 is 0, while in the second proposition the result of test 2 is 1.

Figure 2

(a) Scheme for sequential tests of $x_1$ and $x_2$. The two possible results of each test are assigned the values $+1$ and $-1$, and are represented by whichever lamp is flashing. (b) Cascade setup used to implement two sequential tests on a single photon. It consists of three parts: state preparation, testing devices, and detectors. The preparation part produces the polarization-spatial path-encoded single-photon state $|\psi ⟩$. The two outputs of the device for testing $x_1$ correspond to the two possible results. After each of these two outputs, we placed a device for testing $x_2$. Single-photon detectors are placed at each of the four outputs of the two devices $x_2$ (see the main text for details).

Figure 3

Devices for measuring the six tests defined in (10). The technique used consists of mapping the eigenstates of the operator to the two states $|t,\varphi ⟩$ and $|r,\varphi ⟩$, where $\varphi$ is a polarization state (see the main text for details).